PosterThe Conference on-line proceedings website is located at http://www.lifesciencessociety.org... more PosterThe Conference on-line proceedings website is located at http://www.lifesciencessociety.org/CSB2009/toc
Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assemb... more Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assembly which plays significant roles in many applications remains a great challenge. Most of the state-of-the-art approaches base on de Bruijn graph strategy and overlap-layout strategy. However, these approaches which depend on k-mers or read overlaps do not fully utilize information of single-end and paired-end reads when resolving branches, e.g. the number and positions of reads supporting each possible extension are not taken into account when resolving branches. We present PERGA (Paired-End Reads Guided Assembler), a novel sequence-reads-guided de novo assembly approach, which adopts greedy-like prediction strategy for assembling reads to contigs and scaffolds. Instead of using single-end reads to construct contig, PERGA uses paired-end reads and different read overlap size thresholds ranging from O max to O min to resolve the gaps and branches. Moreover, by constructing a decision model using machine learning approach based on branch features, PERGA can determine the correct extension in 99.7% of cases. When the correct extension cannot be determined, PERGA will try to extend the contigs by all feasible extensions and determine the correct extension by using look ahead technology. We evaluated PERGA on both simulated Illumina data sets and real data sets, and it constructed longer and more correct contigs and scaffolds than other state-of-the-art assemblers IDBA-UD, Velvet, ABySS, SGA and CABOG.
2014 IEEE International Conference on Data Mining, 2014
Bayesian networks (BNs) are popular for modeling conditional distributions of variables and causa... more Bayesian networks (BNs) are popular for modeling conditional distributions of variables and causal relationships, especially in biological settings such as protein interactions, gene regulatory networks and microbial interactions. Previous BN structure learning algorithms treat variables with similar tendency separately. In this paper, we propose a grouped sparse Gaussian BN (GSGBN) structure learning algorithm which creates BN based on three assumptions: (i) variables follow a multivariate Gaussian distribution, (ii) the network only contains a few edges (sparse), (iii) similar variables have less-divergent sets of parents, while not-so-similar ones should have divergent sets of parents (variable grouping). We use L 1 regularization to make the learned network sparse, and another term to incorporate shared information among variables. For similar variables, GSGBN tends to penalize the differences of similar variables' parent sets more, compared to those not-so-similar variables' parent sets. The similarity of variables is learned from the data by alternating optimization, without prior domain knowledge. Based on this new definition of the optimal BN, a coordinate descent algorithm and a projected gradient descent algorithm are developed to obtain edges of the network and also similarity of variables. Experimental results on both simulated and real datasets show that GSGBN has substantially superior prediction performance for structure learning when compared to several existing algorithms.
ABSTRACT Although theLongest Common Subsequence (LCS)Problem has been studied by many researchers... more ABSTRACT Although theLongest Common Subsequence (LCS)Problem has been studied by many researchers for years, heuristic methods have not been investigated before. In this paper we present a simple heuristic which guarantees to return a common subsequence of length at least 1/s that of the longest wheres is the number of different symbols in the input strings. Furthermore, we generalize the idea to several classes of heuristic algorithms. Surprisingly, we find that no other heuristic in these classes outperforms this simple algorithm. In other words, we show that any heuristic which uses only global information, such as number of symbol occurrences, might return a common subsequence as short as 1/s of the length of the longest. Analysis of the average performance of the simple heuristic fors=2 is also presented.
Web caching is an important technology for improving the scalability of Web services. One of the ... more Web caching is an important technology for improving the scalability of Web services. One of the key problems in coordinated enroute Web caching is to compute the locations for storing copies of an object among the enroute caches so that some specified objectives are achieved. In this article, we address this problem for tree networks, and formulate it as a maximization problem. We consider this problem for both unconstrained and constrained cases. The constrained case includes constraints on the cost gain per node and on the number of object copies to be placed. We present dynamic programming-based solutions to this problem for different cases and theoretically show that the solutions are either optimal or convergent to optimal solutions. We derive efficient algorithms that produce these solutions. Based on our mathematical model, we also present a solution to coordinated enroute Web caching for autonomous systems as a natural extension of the solution for tree networks. We impleme...
The security problem of statistical databases containing anonymous but individual records which m... more The security problem of statistical databases containing anonymous but individual records which may be evaluated by queries about sums and averages is considered. A model, more realistic than the previous ones, is proposed, in which nonexisting records for some keys can be allowed. Under the assumption that the system protects the individual's information by the well-known technique which avoids publishing summaries with small counts, several properties about the system and a necessary and sufficient condition for compromising the database have been derived. The minimum number of queries needed to compromise the database is also discussed.
The security problem of a statistical database is to limit the use of the database so that no seq... more The security problem of a statistical database is to limit the use of the database so that no sequence of statistical queries is sufficient to deduce confidential or private information. In this paper it is suggested that the problem be investigated at the conceptual data model level. The design of a statistical database should utilize a statistical security management facility to enforce the security constraints at the conceptual model level. Information revealed to users is well defined in the sense that it can at most be reduced to nondecomposable information involving a group of individuals. In addition, the design also takes into consideration means of storing the query information for auditing purposes, changes in the database, users' knowledge, and some security measures.
A new generating kernel based on cubic B-spline fitting for image pyramids is introduced. This ke... more A new generating kernel based on cubic B-spline fitting for image pyramids is introduced. This kernel is optimal in the sense that the mean square error between images recovered from images compressed with it and the originals is minimized This kernel possesses other attractive properties such as symmetry, normalizational, unimodality, and equal contribution, as well as small window size and fast inverse transformation. Experiments show thal it compares favorably in practical use with other kernels based on piecewise fitting in terms mean square error.
Digital Video Compression: Algorithms and Technologies 1996, 1996
Block matching algorithms (BMAs) are often employed for motion estimation (ME) in video coding. M... more Block matching algorithms (BMAs) are often employed for motion estimation (ME) in video coding. Most conventional BMAs treat the ME problem as an optimization problem and employ certain search schemes to find a solution. Except the time-consuming full search algorithms (FS), other fast algorithms such as the three step search (TSS), searching on a reduced search range, cannot guarantee optimal solutions, i.e., search is often trapped at local minima; the ME results are thus usually unsatisfactory. Few of them makes use of the information inherent in the images explicitly. We propose a new ME algorithm which can reduce the search range while guaranteeing global optimality in most cases. Microblock visual patterns are designed to extract edge information to guide block matching: searching is only carried out at places where the real match most likely happens; that is where similar edge features present. The proposed algorithm obtains a speed about 7 - 8 times as fast as that of FS with same search range. The prediction quality is very close to that of FS and much better than that of TSS. It can produce MPEG-1 or MPEG-2 compatible motion vectors, and can be extended to model-based ME. It is suitable for parallel implementation too. Moreover, the visual patterns are potential resources for video indexing to facilitate content-based information retrieval, which is important for applications such as VOD.
Regulatory Genomics - Proceedings of the 3rd Annual RECOMB Workshop, 2008
The problem of finding motifs in binding sites is very important to the understanding of gene reg... more The problem of finding motifs in binding sites is very important to the understanding of gene regulatory networks. However, when predicting a set of motifs, existing algorithms suffer the problem of either predicting many redundant motifs (motifs with similar binding sites) or, at the other extreme, missing the hidden motif. In this paper, we formulate the Motif Redundancy Problem (MRP) to model this kind of problem and introduce an algorithm called RME (Redundancy Motif Elimination) for solving MRP. Experimental results on real biological data show that a standard EM-based motif discovery algorithm enhanced with RME has a better performance than the popular motif discovery algorithm MEME.
1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings
Block matching algorithms(BMAs) are often employed for motion estimation(ME) in video coding. Mos... more Block matching algorithms(BMAs) are often employed for motion estimation(ME) in video coding. Most conventional fast BMAs treat the ME problem as an optimization problem and suffer heavily from the problem of being trapped at local minima. The full search algorithm(FS), on the other hand, is very time-consuming. Few of them makes use of the information inherent in the images explicitly. We propose a new ME algorithm which can reduce the search range while guaranteeing global optimality in most cases, making use of the edge features. Microblock visual patterns are designed to extract edge information to guide block matching: searching is only carried out at places where the real match most likely happens. The motion field subsampling technique is further employed to get a hierarchical algorithm, which can further double the speed. The proposed algorithms obtain speeds about t,en times faster than that of FS with comparable prediction quality.
Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove sev... more Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahedralizations. We present an O(nm log n) algorithm to determine whether L is the edge set of a tetrahedralization, where m is the number of segments and n is the number of endpoints in L. We show that it is NP-complete to decide whether L contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether L is tetrahedralizable.
Sixth IEEE Symposium on BioInformatics and BioEngineering (BIBE'06), 2006
ABSTRACT The problem of finding motifs of binding sites is very important to the understanding of... more ABSTRACT The problem of finding motifs of binding sites is very important to the understanding of gene regulatory networks. Motifs are generally represented by matrices (PWM or PSSM) or strings. However, these representations cannot model biological binding sites well because they fail to capture nucleotide interdependence. It has been pointed out by many researchers that the nucleotides of the DNA binding site cannot be treated independently, e.g. the binding of zinc finger in proteins. In this paper, a new representation called Scored Position Specific Pattern (SPSP), which is a generalization of the matrix and string representations, is introduced which takes into consideration the dependent occurrences of neighboring nucleotides. Even though the problem of finding the optimal motif in SPSP representation is proved to be NP-hard, we introduce a heuristic algorithm called SPSP-Finder, which can effectively find optimal motifs in most simulated cases and some real cases for which existing popular motif-finding software, such as MEME and AlignACE fail
A generalized problem is defined in terms of functions on sets and illustrated in terms of the co... more A generalized problem is defined in terms of functions on sets and illustrated in terms of the computational geometry of simple planar polygons. Although its apparent time complexity is O (n2), the problem is shown to be solvable for several cases of interest (maximum and minimum distance, intersection detection and rerporting) in O (n log n), O (n), or O (log n) time, depending on the nature of a specialized "selection" function. (Some of the cases can also be solved by the Voronoi diagram method; but time complexity increases with that approach.) A new use of monotonicity and a new concept of" locality" in set mappings contribute significantly to the derivation of the results.
We address the problem of maintaining the distributed database consistency in presence of failure... more We address the problem of maintaining the distributed database consistency in presence of failures while maximizing the database availability. Network Partitioning is a failure which partitions the distributed system into a number of parts, no part being able to communicate with any other. Formalizations of various notions in this context are developed and two measures for the performances of protocols in presence of a network partitioning are introduced. A general optimality theory is developed for two classes of protocols-centralized and decentralized. Optimal protocols are produced in all cases. Key words, commit protocols, consistency, database availability, distributed databases, fault-tolerance, network partitioning, optimal protocals, transaction processing 1. Introduction. A database DB consists of a collection of entities D= {dl, d2," '', din} such that each di in D has a value set V associated to it, and a set R of relations r on Xi=l V which we call consistency constraints for DB. An instance of the database DB is an element from Xi=l V. An instance (Vl, v2,"" ", v,) of DB is consistent if and only if (Vl, v2,'' ", Vm) is in r for all r in R. User programs map the set of database instances into itself. We are primarily interested in those programs that map the set of consistent database instances into itself. Executions of such programs are known as transactions and play the central role in database literature [10], [12]. Formally, a transaction is an execution of a (user) program, t'X=l V-> X=I v such that for any consistent instance I, t(I) is also consistent. If only a sequence of transactions is allowed to operate on a consistent database instance, then the final instance is also guaranteed to be consistent. We require that all transactions are ensured that the instances they are going to operate on are consistent. This guarantees the database consistency, without any need for an explicit validation of the consistency constraints. Several mechanisms are available which guarantee .that any transaction sees an initial consistent instance and can map the set of consistent DB instances into itself even if several transactions are being concurrently run. See [2], [3] for a comprehensive survey on this area. Without loss of generality, assume that, if O1, O2,'", Ok is the sequence of operations in a transaction, then no subsequence O1, 02, , Op, 1 <= p < k, guarantees the resulting database instance to be consistent. At the implementation level, this would imply that, given a consistent instance I1 of DB, a transaction acting on I1 would lead to a consistent instance I_ if and only if either does not modify I1 or all modifications made by are incorporated onto I1. Such an implementation of a transaction is known as atomic implementation [12]. Thus, a transaction can legally be completed in only one of two possible modes-either it is committed in which case all its effects are incorporated into the database instance, or it is aborted in which case none of its effects are incorporated. A distributed system is an undirected connected graph (3 (V, E). Each node represents a site consisting of a processor and possibly storage and other modules. Each edge represents a communication link. A database is said to be distributed if it physically resides at more than one site. That is, each site contains a subset of the database entities. We make no assumptions on the degree of replication-each entity *
In this paper, we present an Θ(n) time worst-case deterministic algorithm for finding the constra... more In this paper, we present an Θ(n) time worst-case deterministic algorithm for finding the constrained Delaunay triangulation and constrained Voronoi diagram of a simple n-sided polygon in the plane. Up to now, only an O(n log n) worst-case deterministic and an O(n) expected time bound have been shown, leaving an O(n) deterministic solution open to conjecture.
The basic inference problem is defined as follows: For a finite set X = { x i , … , x n }, we wis... more The basic inference problem is defined as follows: For a finite set X = { x i , … , x n }, we wish to infer properties of elements of X on the basis of sets of "queries" regarding subsets of X . By restricting these queries to statistical queries, the statistical database (SDB) security problem is obtained. The security problem for the SDB is to limit the use of the SDB so that only statistical information is available and no sequence of queries is sufficient to infer protected information about any individual. When such information is obtained the SDB is said to be compromised. In this paper, two applications concerning the security of the SDB are considered: On-line application . The queries are answered one by one in sequence and it is necessary to determine whether the SDB is compromised if a new query is answered. Off-line application . All queries are available at the same time and it is necessary to determine the maximum subset of queries to be answered without comp...
International Journal of Computer Mathematics, 1984
An optimal solution is presented for the scheduling of printing and binding of a book order. The ... more An optimal solution is presented for the scheduling of printing and binding of a book order. The algorithm is simpler and faster than previously known methods. If the book is divided into n parts and the typesetting time for each part is different, the algorithm takes steps. The algorithm operates in linear time if all the typesetting times are identical. The problem can be generalized easily to other problems and its optimal solution can be applied to other two-stage production processes with overheads for interruptions.
PosterThe Conference on-line proceedings website is located at http://www.lifesciencessociety.org... more PosterThe Conference on-line proceedings website is located at http://www.lifesciencessociety.org/CSB2009/toc
Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assemb... more Since the read lengths of high throughput sequencing (HTS) technologies are short, de novo assembly which plays significant roles in many applications remains a great challenge. Most of the state-of-the-art approaches base on de Bruijn graph strategy and overlap-layout strategy. However, these approaches which depend on k-mers or read overlaps do not fully utilize information of single-end and paired-end reads when resolving branches, e.g. the number and positions of reads supporting each possible extension are not taken into account when resolving branches. We present PERGA (Paired-End Reads Guided Assembler), a novel sequence-reads-guided de novo assembly approach, which adopts greedy-like prediction strategy for assembling reads to contigs and scaffolds. Instead of using single-end reads to construct contig, PERGA uses paired-end reads and different read overlap size thresholds ranging from O max to O min to resolve the gaps and branches. Moreover, by constructing a decision model using machine learning approach based on branch features, PERGA can determine the correct extension in 99.7% of cases. When the correct extension cannot be determined, PERGA will try to extend the contigs by all feasible extensions and determine the correct extension by using look ahead technology. We evaluated PERGA on both simulated Illumina data sets and real data sets, and it constructed longer and more correct contigs and scaffolds than other state-of-the-art assemblers IDBA-UD, Velvet, ABySS, SGA and CABOG.
2014 IEEE International Conference on Data Mining, 2014
Bayesian networks (BNs) are popular for modeling conditional distributions of variables and causa... more Bayesian networks (BNs) are popular for modeling conditional distributions of variables and causal relationships, especially in biological settings such as protein interactions, gene regulatory networks and microbial interactions. Previous BN structure learning algorithms treat variables with similar tendency separately. In this paper, we propose a grouped sparse Gaussian BN (GSGBN) structure learning algorithm which creates BN based on three assumptions: (i) variables follow a multivariate Gaussian distribution, (ii) the network only contains a few edges (sparse), (iii) similar variables have less-divergent sets of parents, while not-so-similar ones should have divergent sets of parents (variable grouping). We use L 1 regularization to make the learned network sparse, and another term to incorporate shared information among variables. For similar variables, GSGBN tends to penalize the differences of similar variables' parent sets more, compared to those not-so-similar variables' parent sets. The similarity of variables is learned from the data by alternating optimization, without prior domain knowledge. Based on this new definition of the optimal BN, a coordinate descent algorithm and a projected gradient descent algorithm are developed to obtain edges of the network and also similarity of variables. Experimental results on both simulated and real datasets show that GSGBN has substantially superior prediction performance for structure learning when compared to several existing algorithms.
ABSTRACT Although theLongest Common Subsequence (LCS)Problem has been studied by many researchers... more ABSTRACT Although theLongest Common Subsequence (LCS)Problem has been studied by many researchers for years, heuristic methods have not been investigated before. In this paper we present a simple heuristic which guarantees to return a common subsequence of length at least 1/s that of the longest wheres is the number of different symbols in the input strings. Furthermore, we generalize the idea to several classes of heuristic algorithms. Surprisingly, we find that no other heuristic in these classes outperforms this simple algorithm. In other words, we show that any heuristic which uses only global information, such as number of symbol occurrences, might return a common subsequence as short as 1/s of the length of the longest. Analysis of the average performance of the simple heuristic fors=2 is also presented.
Web caching is an important technology for improving the scalability of Web services. One of the ... more Web caching is an important technology for improving the scalability of Web services. One of the key problems in coordinated enroute Web caching is to compute the locations for storing copies of an object among the enroute caches so that some specified objectives are achieved. In this article, we address this problem for tree networks, and formulate it as a maximization problem. We consider this problem for both unconstrained and constrained cases. The constrained case includes constraints on the cost gain per node and on the number of object copies to be placed. We present dynamic programming-based solutions to this problem for different cases and theoretically show that the solutions are either optimal or convergent to optimal solutions. We derive efficient algorithms that produce these solutions. Based on our mathematical model, we also present a solution to coordinated enroute Web caching for autonomous systems as a natural extension of the solution for tree networks. We impleme...
The security problem of statistical databases containing anonymous but individual records which m... more The security problem of statistical databases containing anonymous but individual records which may be evaluated by queries about sums and averages is considered. A model, more realistic than the previous ones, is proposed, in which nonexisting records for some keys can be allowed. Under the assumption that the system protects the individual's information by the well-known technique which avoids publishing summaries with small counts, several properties about the system and a necessary and sufficient condition for compromising the database have been derived. The minimum number of queries needed to compromise the database is also discussed.
The security problem of a statistical database is to limit the use of the database so that no seq... more The security problem of a statistical database is to limit the use of the database so that no sequence of statistical queries is sufficient to deduce confidential or private information. In this paper it is suggested that the problem be investigated at the conceptual data model level. The design of a statistical database should utilize a statistical security management facility to enforce the security constraints at the conceptual model level. Information revealed to users is well defined in the sense that it can at most be reduced to nondecomposable information involving a group of individuals. In addition, the design also takes into consideration means of storing the query information for auditing purposes, changes in the database, users' knowledge, and some security measures.
A new generating kernel based on cubic B-spline fitting for image pyramids is introduced. This ke... more A new generating kernel based on cubic B-spline fitting for image pyramids is introduced. This kernel is optimal in the sense that the mean square error between images recovered from images compressed with it and the originals is minimized This kernel possesses other attractive properties such as symmetry, normalizational, unimodality, and equal contribution, as well as small window size and fast inverse transformation. Experiments show thal it compares favorably in practical use with other kernels based on piecewise fitting in terms mean square error.
Digital Video Compression: Algorithms and Technologies 1996, 1996
Block matching algorithms (BMAs) are often employed for motion estimation (ME) in video coding. M... more Block matching algorithms (BMAs) are often employed for motion estimation (ME) in video coding. Most conventional BMAs treat the ME problem as an optimization problem and employ certain search schemes to find a solution. Except the time-consuming full search algorithms (FS), other fast algorithms such as the three step search (TSS), searching on a reduced search range, cannot guarantee optimal solutions, i.e., search is often trapped at local minima; the ME results are thus usually unsatisfactory. Few of them makes use of the information inherent in the images explicitly. We propose a new ME algorithm which can reduce the search range while guaranteeing global optimality in most cases. Microblock visual patterns are designed to extract edge information to guide block matching: searching is only carried out at places where the real match most likely happens; that is where similar edge features present. The proposed algorithm obtains a speed about 7 - 8 times as fast as that of FS with same search range. The prediction quality is very close to that of FS and much better than that of TSS. It can produce MPEG-1 or MPEG-2 compatible motion vectors, and can be extended to model-based ME. It is suitable for parallel implementation too. Moreover, the visual patterns are potential resources for video indexing to facilitate content-based information retrieval, which is important for applications such as VOD.
Regulatory Genomics - Proceedings of the 3rd Annual RECOMB Workshop, 2008
The problem of finding motifs in binding sites is very important to the understanding of gene reg... more The problem of finding motifs in binding sites is very important to the understanding of gene regulatory networks. However, when predicting a set of motifs, existing algorithms suffer the problem of either predicting many redundant motifs (motifs with similar binding sites) or, at the other extreme, missing the hidden motif. In this paper, we formulate the Motif Redundancy Problem (MRP) to model this kind of problem and introduce an algorithm called RME (Redundancy Motif Elimination) for solving MRP. Experimental results on real biological data show that a standard EM-based motif discovery algorithm enhanced with RME has a better performance than the popular motif discovery algorithm MEME.
1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings
Block matching algorithms(BMAs) are often employed for motion estimation(ME) in video coding. Mos... more Block matching algorithms(BMAs) are often employed for motion estimation(ME) in video coding. Most conventional fast BMAs treat the ME problem as an optimization problem and suffer heavily from the problem of being trapped at local minima. The full search algorithm(FS), on the other hand, is very time-consuming. Few of them makes use of the information inherent in the images explicitly. We propose a new ME algorithm which can reduce the search range while guaranteeing global optimality in most cases, making use of the edge features. Microblock visual patterns are designed to extract edge information to guide block matching: searching is only carried out at places where the real match most likely happens. The motion field subsampling technique is further employed to get a hierarchical algorithm, which can further double the speed. The proposed algorithms obtain speeds about t,en times faster than that of FS with comparable prediction quality.
Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove sev... more Let L be a set of line segments in three dimensional Euclidean space. In this paper, we prove several characterizations of tetrahedralizations. We present an O(nm log n) algorithm to determine whether L is the edge set of a tetrahedralization, where m is the number of segments and n is the number of endpoints in L. We show that it is NP-complete to decide whether L contains the edge set of a tetrahedralization. We also show that it is NP-complete to decide whether L is tetrahedralizable.
Sixth IEEE Symposium on BioInformatics and BioEngineering (BIBE'06), 2006
ABSTRACT The problem of finding motifs of binding sites is very important to the understanding of... more ABSTRACT The problem of finding motifs of binding sites is very important to the understanding of gene regulatory networks. Motifs are generally represented by matrices (PWM or PSSM) or strings. However, these representations cannot model biological binding sites well because they fail to capture nucleotide interdependence. It has been pointed out by many researchers that the nucleotides of the DNA binding site cannot be treated independently, e.g. the binding of zinc finger in proteins. In this paper, a new representation called Scored Position Specific Pattern (SPSP), which is a generalization of the matrix and string representations, is introduced which takes into consideration the dependent occurrences of neighboring nucleotides. Even though the problem of finding the optimal motif in SPSP representation is proved to be NP-hard, we introduce a heuristic algorithm called SPSP-Finder, which can effectively find optimal motifs in most simulated cases and some real cases for which existing popular motif-finding software, such as MEME and AlignACE fail
A generalized problem is defined in terms of functions on sets and illustrated in terms of the co... more A generalized problem is defined in terms of functions on sets and illustrated in terms of the computational geometry of simple planar polygons. Although its apparent time complexity is O (n2), the problem is shown to be solvable for several cases of interest (maximum and minimum distance, intersection detection and rerporting) in O (n log n), O (n), or O (log n) time, depending on the nature of a specialized "selection" function. (Some of the cases can also be solved by the Voronoi diagram method; but time complexity increases with that approach.) A new use of monotonicity and a new concept of" locality" in set mappings contribute significantly to the derivation of the results.
We address the problem of maintaining the distributed database consistency in presence of failure... more We address the problem of maintaining the distributed database consistency in presence of failures while maximizing the database availability. Network Partitioning is a failure which partitions the distributed system into a number of parts, no part being able to communicate with any other. Formalizations of various notions in this context are developed and two measures for the performances of protocols in presence of a network partitioning are introduced. A general optimality theory is developed for two classes of protocols-centralized and decentralized. Optimal protocols are produced in all cases. Key words, commit protocols, consistency, database availability, distributed databases, fault-tolerance, network partitioning, optimal protocals, transaction processing 1. Introduction. A database DB consists of a collection of entities D= {dl, d2," '', din} such that each di in D has a value set V associated to it, and a set R of relations r on Xi=l V which we call consistency constraints for DB. An instance of the database DB is an element from Xi=l V. An instance (Vl, v2,"" ", v,) of DB is consistent if and only if (Vl, v2,'' ", Vm) is in r for all r in R. User programs map the set of database instances into itself. We are primarily interested in those programs that map the set of consistent database instances into itself. Executions of such programs are known as transactions and play the central role in database literature [10], [12]. Formally, a transaction is an execution of a (user) program, t'X=l V-> X=I v such that for any consistent instance I, t(I) is also consistent. If only a sequence of transactions is allowed to operate on a consistent database instance, then the final instance is also guaranteed to be consistent. We require that all transactions are ensured that the instances they are going to operate on are consistent. This guarantees the database consistency, without any need for an explicit validation of the consistency constraints. Several mechanisms are available which guarantee .that any transaction sees an initial consistent instance and can map the set of consistent DB instances into itself even if several transactions are being concurrently run. See [2], [3] for a comprehensive survey on this area. Without loss of generality, assume that, if O1, O2,'", Ok is the sequence of operations in a transaction, then no subsequence O1, 02, , Op, 1 <= p < k, guarantees the resulting database instance to be consistent. At the implementation level, this would imply that, given a consistent instance I1 of DB, a transaction acting on I1 would lead to a consistent instance I_ if and only if either does not modify I1 or all modifications made by are incorporated onto I1. Such an implementation of a transaction is known as atomic implementation [12]. Thus, a transaction can legally be completed in only one of two possible modes-either it is committed in which case all its effects are incorporated into the database instance, or it is aborted in which case none of its effects are incorporated. A distributed system is an undirected connected graph (3 (V, E). Each node represents a site consisting of a processor and possibly storage and other modules. Each edge represents a communication link. A database is said to be distributed if it physically resides at more than one site. That is, each site contains a subset of the database entities. We make no assumptions on the degree of replication-each entity *
In this paper, we present an Θ(n) time worst-case deterministic algorithm for finding the constra... more In this paper, we present an Θ(n) time worst-case deterministic algorithm for finding the constrained Delaunay triangulation and constrained Voronoi diagram of a simple n-sided polygon in the plane. Up to now, only an O(n log n) worst-case deterministic and an O(n) expected time bound have been shown, leaving an O(n) deterministic solution open to conjecture.
The basic inference problem is defined as follows: For a finite set X = { x i , … , x n }, we wis... more The basic inference problem is defined as follows: For a finite set X = { x i , … , x n }, we wish to infer properties of elements of X on the basis of sets of "queries" regarding subsets of X . By restricting these queries to statistical queries, the statistical database (SDB) security problem is obtained. The security problem for the SDB is to limit the use of the SDB so that only statistical information is available and no sequence of queries is sufficient to infer protected information about any individual. When such information is obtained the SDB is said to be compromised. In this paper, two applications concerning the security of the SDB are considered: On-line application . The queries are answered one by one in sequence and it is necessary to determine whether the SDB is compromised if a new query is answered. Off-line application . All queries are available at the same time and it is necessary to determine the maximum subset of queries to be answered without comp...
International Journal of Computer Mathematics, 1984
An optimal solution is presented for the scheduling of printing and binding of a book order. The ... more An optimal solution is presented for the scheduling of printing and binding of a book order. The algorithm is simpler and faster than previously known methods. If the book is divided into n parts and the typesetting time for each part is different, the algorithm takes steps. The algorithm operates in linear time if all the typesetting times are identical. The problem can be generalized easily to other problems and its optimal solution can be applied to other two-stage production processes with overheads for interruptions.
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Papers by Francis Chin