The stretch constraint occurs in many rostering problems that arise in the industrial and public ... more The stretch constraint occurs in many rostering problems that arise in the industrial and public service sectors. In this paper we present an efficient algorithm for domain consistency propagation of the stretch constraint. Using benchmark and random instances, we show that this stronger consistency sometimes enables our propagator to solve more difficult problems than a previously proposed propagation algorithm for the stretch constraint. We also discuss variations of the stretch constraint that seem simple and useful, but turn out to be intractable to fully propagate.
One of the main reasons why constraint programming quickly found its way into applications has be... more One of the main reasons why constraint programming quickly found its way into applications has been the early availability of usable constraint programming systems. Given the wide range of applications using constraint programming it is obvious that one of the key properties of constraint programming systems is their provision of widely reusable services for constructing constraint-based applications. A constraint programming system can be thought of as providing a set of reusable services. Common services include constraint propagation, search, and services for interfacing to the system. This chapter looks in more detail at which services are provided by a constraint programming system and in particular what are the key principles and techniques in constructing and coordinating these services.
19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007), 2007
Constraint satisfaction and propositional satisfiability problems are often solved using backtrac... more Constraint satisfaction and propositional satisfiability problems are often solved using backtracking search. Previous studies have shown that portfolios of backtracking algorithms-a selection of one or more algorithms plus a schedule for executing the algorithms-can dramatically improve performance on some instances. In this paper, we consider a setting that often arises in practice where the instances to be solved arise over time, the instances all belong to some class of problem instances, and a limit or deadline is placed on the computational resources that the backtracking algorithm can consume in solving any instance. For such a scenario, we present a simple scheme for learning a good portfolio of backtracking algorithms from a small sample of instances. We demonstrate the effectiveness of our approach through an extensive empirical evaluation on a real-world instruction scheduling testbed.
Plan recognition is the processof inferring a plausible set of plans that explain an agent's ... more Plan recognition is the processof inferring a plausible set of plans that explain an agent's actions. In this paper, I use a small example to focus on some non-probabilistic heuristics proposed in the literature for preferring one plan over an- other. I show some of the conditions or constraints on the probability distributions so that the plan that is preferred
We present a new property called constraint looseness and show how it can be used to estimate the... more We present a new property called constraint looseness and show how it can be used to estimate thelevel of local consistency of a binary constraint network.Specifically, we present a relationship betweenthe looseness of the constraints, the size of the domains,and the inherent level of local consistency of aconstraint network. The results we present are usefulin two ways. First, a common method for finding solutionsto a constraint network is to first preprocess thenetwork by enforcing...
Constraint programming is a powerful paradigm for solving combinatorial search problems that draw... more Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence (AI), operations research, algorithms, and graph theory. The basic idea in constraint programming is that the user states the constraints, and a general-purpose constraint solver is used to solve them. Constraints are just relations, and a constraint satisfaction problem (CSP) states the relations that should hold among the given decision variables. A constraint satisfaction problem consists of a set of variables, each with some domain of values, and a set of relations on the subsets of these variables. For example, in scheduling exams at a university, the decision variables might be the times and locations of different exams, and the constraints might be on the capacity of each examination room (e.g., we cannot schedule more students to sit for exams in a given room at any one time than the room's capacity) and on the exams scheduled at the same time (e.g., we cannot schedule two exams at the same time if they share students in common). Constraint solvers take a real-world problem like this represented in terms of decision variables and constraints and find an assignment to all the variables that satisfies the constraints. Extensions of this framework may involve, for example, finding optimal solutions according to one or more optimization criterion (e.g., minimizing the number of days over which exams need to be scheduled), finding all solutions, replacing (some or all) constraints with preferences, and considering a distributed setting where constraints are distributed among several agents.
Constraint networks have been shown to be usefulin formulating such diverse problems as scenelabe... more Constraint networks have been shown to be usefulin formulating such diverse problems as scenelabeling, natural language parsing, and temporalreasoning. Given a constraint network, we oftenwish to (i) find a solution that satisfies the constraintsand (ii) find the corresponding minimalnetwork where the constraints are as explicit aspossible. Both tasks are known to be NP-completein the general case. Task (i) is usually solved usinga backtracking algorithm, and task (ii) is oftensolved...
Constraint networks are a simple representation and reasoning framework with diverse applications... more Constraint networks are a simple representation and reasoning framework with diverse applications. In this paper, we identify two new complementary properties on the restrictiveness of the constraints in a networkconstraint tightness and constraint looseness-and we show their usefulness for estimating the level of local consistency needed to ensure global consistency, and for estimating the level of local consistency present in a network. In particular, we present a sufficient condition, based on constraint tightness and the level of local consistency, that guarantees that a solution can be found in a backtrack-free manner. The condition can be useful in applications where a knowledge base will be queried over and over and the preprocessing costs can be amortized over many queries. We also present a sufficient condition for local consistency, based on constraint looseness, that is straightforward and inexpensive to determine. The condition can be used to estimate the level of local consistency of a network. This in turn can be used in deciding whether it would be useful to preprocess the network before a backtracking search, and in deciding which local consistency conditions, if any, still need to be enforced if we want to ensure that a solution can be found in a backtrack-free manner. Two definitions of local consistency are employed in characterizing the conditions: the traditional variable-based notion and a recently introduced definition of local consistency called relational consistency 1 .
â–º We model NHL qualification and elimination problems. â–º We solve the problems using constrai... more â–º We model NHL qualification and elimination problems. â–º We solve the problems using constraint programming and enumeration. â–º Our phased approach is an efficient technique for solving these problems.
The annual conference on the Principles and Practice of Constraint Programming was held at Cornel... more The annual conference on the Principles and Practice of Constraint Programming was held at Cornell University in 2002. The conference attracted a record number of submissions (which has been broken since then) and featured a high-quality technical program covering many aspects of constraint programming.
Interval and point algebras have been proposed for representing qualitative temporal information ... more Interval and point algebras have been proposed for representing qualitative temporal information about the relationships between pairs of intervals and pairs of points, respectively. In this paper, we address two related reasoning tasks that arise in these algebras : Given (possibly indefinite) knowledge of the relationships between some intervals or points, (1) find one or more scenarios that are consistent with the information provided, and (2) find all the feasible relations between every pair of intervals or points . Solutions to these problems have applications in natural language processing, planning, and a knowledge representation language . We define computationally efficient procedures for solving these tasks for the point algebra and for a corresponding subset of the interval algebra. Our algorithms are marked improvements over the previously known algorithms . We also show how the results for the point algebra help us to design a backtracking algorithm for the full interval algebra that is useful in practice .
The general solution of satisfiability problems is NP-Complete. Although state-of-the-art SAT sol... more The general solution of satisfiability problems is NP-Complete. Although state-of-the-art SAT solvers can efficiently obtain the solutions of many real-world instances, there are still a large number of real-world SAT families which cannot be solved in reasonable time. Much effort has been spent to take advantage of the internal structure of SAT instances. Existing decomposition techniques are based on preprocessing the static structure of the original problem. We present a dynamic decomposition method based on hypergraph separators. Integrating the separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real-world satisfiability problems. Compared with a static decomposition based variable ordering, such as Dtree , our approach does not need time to construct the full tree decomposition, which sometimes needs more time than the solving process itself. Our primary focus is to achieve speedups on large real-world satisfiability problems. Our results show that the new solver often outperforms both regular zChaff and zChaff integrated with Dtree decomposition. The dynamic separator decomposition shows promise in that it significantly decreases the number of decisions for some real-world problems.
In recent years, many new backtracking algorithms for solving constraint satisfaction problems ha... more In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a different, purely theoretical approach, which is based on characterizations of the sets of search tree nodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such wellknown concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove, for the rst time, the correctness of Backjumping and Con ict-Directed Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ict-Directed Backjumping (BM-CBJ), so that they always perform fewer consistency checks than the original algorithms.
The stretch constraint occurs in many rostering problems that arise in the industrial and public ... more The stretch constraint occurs in many rostering problems that arise in the industrial and public service sectors. In this paper we present an efficient algorithm for domain consistency propagation of the stretch constraint. Using benchmark and random instances, we show that this stronger consistency sometimes enables our propagator to solve more difficult problems than a previously proposed propagation algorithm for the stretch constraint. We also discuss variations of the stretch constraint that seem simple and useful, but turn out to be intractable to fully propagate.
One of the main reasons why constraint programming quickly found its way into applications has be... more One of the main reasons why constraint programming quickly found its way into applications has been the early availability of usable constraint programming systems. Given the wide range of applications using constraint programming it is obvious that one of the key properties of constraint programming systems is their provision of widely reusable services for constructing constraint-based applications. A constraint programming system can be thought of as providing a set of reusable services. Common services include constraint propagation, search, and services for interfacing to the system. This chapter looks in more detail at which services are provided by a constraint programming system and in particular what are the key principles and techniques in constructing and coordinating these services.
19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007), 2007
Constraint satisfaction and propositional satisfiability problems are often solved using backtrac... more Constraint satisfaction and propositional satisfiability problems are often solved using backtracking search. Previous studies have shown that portfolios of backtracking algorithms-a selection of one or more algorithms plus a schedule for executing the algorithms-can dramatically improve performance on some instances. In this paper, we consider a setting that often arises in practice where the instances to be solved arise over time, the instances all belong to some class of problem instances, and a limit or deadline is placed on the computational resources that the backtracking algorithm can consume in solving any instance. For such a scenario, we present a simple scheme for learning a good portfolio of backtracking algorithms from a small sample of instances. We demonstrate the effectiveness of our approach through an extensive empirical evaluation on a real-world instruction scheduling testbed.
Plan recognition is the processof inferring a plausible set of plans that explain an agent's ... more Plan recognition is the processof inferring a plausible set of plans that explain an agent's actions. In this paper, I use a small example to focus on some non-probabilistic heuristics proposed in the literature for preferring one plan over an- other. I show some of the conditions or constraints on the probability distributions so that the plan that is preferred
We present a new property called constraint looseness and show how it can be used to estimate the... more We present a new property called constraint looseness and show how it can be used to estimate thelevel of local consistency of a binary constraint network.Specifically, we present a relationship betweenthe looseness of the constraints, the size of the domains,and the inherent level of local consistency of aconstraint network. The results we present are usefulin two ways. First, a common method for finding solutionsto a constraint network is to first preprocess thenetwork by enforcing...
Constraint programming is a powerful paradigm for solving combinatorial search problems that draw... more Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence (AI), operations research, algorithms, and graph theory. The basic idea in constraint programming is that the user states the constraints, and a general-purpose constraint solver is used to solve them. Constraints are just relations, and a constraint satisfaction problem (CSP) states the relations that should hold among the given decision variables. A constraint satisfaction problem consists of a set of variables, each with some domain of values, and a set of relations on the subsets of these variables. For example, in scheduling exams at a university, the decision variables might be the times and locations of different exams, and the constraints might be on the capacity of each examination room (e.g., we cannot schedule more students to sit for exams in a given room at any one time than the room's capacity) and on the exams scheduled at the same time (e.g., we cannot schedule two exams at the same time if they share students in common). Constraint solvers take a real-world problem like this represented in terms of decision variables and constraints and find an assignment to all the variables that satisfies the constraints. Extensions of this framework may involve, for example, finding optimal solutions according to one or more optimization criterion (e.g., minimizing the number of days over which exams need to be scheduled), finding all solutions, replacing (some or all) constraints with preferences, and considering a distributed setting where constraints are distributed among several agents.
Constraint networks have been shown to be usefulin formulating such diverse problems as scenelabe... more Constraint networks have been shown to be usefulin formulating such diverse problems as scenelabeling, natural language parsing, and temporalreasoning. Given a constraint network, we oftenwish to (i) find a solution that satisfies the constraintsand (ii) find the corresponding minimalnetwork where the constraints are as explicit aspossible. Both tasks are known to be NP-completein the general case. Task (i) is usually solved usinga backtracking algorithm, and task (ii) is oftensolved...
Constraint networks are a simple representation and reasoning framework with diverse applications... more Constraint networks are a simple representation and reasoning framework with diverse applications. In this paper, we identify two new complementary properties on the restrictiveness of the constraints in a networkconstraint tightness and constraint looseness-and we show their usefulness for estimating the level of local consistency needed to ensure global consistency, and for estimating the level of local consistency present in a network. In particular, we present a sufficient condition, based on constraint tightness and the level of local consistency, that guarantees that a solution can be found in a backtrack-free manner. The condition can be useful in applications where a knowledge base will be queried over and over and the preprocessing costs can be amortized over many queries. We also present a sufficient condition for local consistency, based on constraint looseness, that is straightforward and inexpensive to determine. The condition can be used to estimate the level of local consistency of a network. This in turn can be used in deciding whether it would be useful to preprocess the network before a backtracking search, and in deciding which local consistency conditions, if any, still need to be enforced if we want to ensure that a solution can be found in a backtrack-free manner. Two definitions of local consistency are employed in characterizing the conditions: the traditional variable-based notion and a recently introduced definition of local consistency called relational consistency 1 .
â–º We model NHL qualification and elimination problems. â–º We solve the problems using constrai... more â–º We model NHL qualification and elimination problems. â–º We solve the problems using constraint programming and enumeration. â–º Our phased approach is an efficient technique for solving these problems.
The annual conference on the Principles and Practice of Constraint Programming was held at Cornel... more The annual conference on the Principles and Practice of Constraint Programming was held at Cornell University in 2002. The conference attracted a record number of submissions (which has been broken since then) and featured a high-quality technical program covering many aspects of constraint programming.
Interval and point algebras have been proposed for representing qualitative temporal information ... more Interval and point algebras have been proposed for representing qualitative temporal information about the relationships between pairs of intervals and pairs of points, respectively. In this paper, we address two related reasoning tasks that arise in these algebras : Given (possibly indefinite) knowledge of the relationships between some intervals or points, (1) find one or more scenarios that are consistent with the information provided, and (2) find all the feasible relations between every pair of intervals or points . Solutions to these problems have applications in natural language processing, planning, and a knowledge representation language . We define computationally efficient procedures for solving these tasks for the point algebra and for a corresponding subset of the interval algebra. Our algorithms are marked improvements over the previously known algorithms . We also show how the results for the point algebra help us to design a backtracking algorithm for the full interval algebra that is useful in practice .
The general solution of satisfiability problems is NP-Complete. Although state-of-the-art SAT sol... more The general solution of satisfiability problems is NP-Complete. Although state-of-the-art SAT solvers can efficiently obtain the solutions of many real-world instances, there are still a large number of real-world SAT families which cannot be solved in reasonable time. Much effort has been spent to take advantage of the internal structure of SAT instances. Existing decomposition techniques are based on preprocessing the static structure of the original problem. We present a dynamic decomposition method based on hypergraph separators. Integrating the separator decomposition into the variable ordering of a modern SAT solver leads to speedups on large real-world satisfiability problems. Compared with a static decomposition based variable ordering, such as Dtree , our approach does not need time to construct the full tree decomposition, which sometimes needs more time than the solving process itself. Our primary focus is to achieve speedups on large real-world satisfiability problems. Our results show that the new solver often outperforms both regular zChaff and zChaff integrated with Dtree decomposition. The dynamic separator decomposition shows promise in that it significantly decreases the number of decisions for some real-world problems.
In recent years, many new backtracking algorithms for solving constraint satisfaction problems ha... more In recent years, many new backtracking algorithms for solving constraint satisfaction problems have been proposed. The algorithms are usually evaluated by empirical testing. This method, however, has its limitations. Our paper adopts a different, purely theoretical approach, which is based on characterizations of the sets of search tree nodes visited by the backtracking algorithms. A notion of inconsistency between instantiations and variables is introduced, and is shown to be a useful tool for characterizing such wellknown concepts as backtrack, backjump, and domain annihilation. The characterizations enable us to: (a) prove the correctness of the algorithms, and (b) partially order the algorithms according to two standard performance measures: the number of nodes visited, and the number of consistency checks performed. Among other results, we prove, for the rst time, the correctness of Backjumping and Con ict-Directed Backjumping, and show that Forward Checking never visits more nodes than Backjumping. Our approach leads us also to propose a modi cation to two hybrid backtracking algorithms, Backmarking with Backjumping (BMJ) and Backmarking with Con ict-Directed Backjumping (BM-CBJ), so that they always perform fewer consistency checks than the original algorithms.
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Papers by Peter van Beek