Papers by Konrad Piwakowski
Lecture Notes in Computer Science, 2002
This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to... more This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to minimize mean flow time. Since the general problem is strongly NP-hard, we assume some restrictions on task lengths and the structure of associated scheduling graphs. Of particular interest are acyclic graphs. In this way we identify a borderline between NP-hard and polynomially solvable special cases.
The electronic journal of combinatorics
For given graphs G 1 , G 2 , ..., G k , where k ≥ 2, the multicolor Ramsey number R(G 1 , G 2 , .... more For given graphs G 1 , G 2 , ..., G k , where k ≥ 2, the multicolor Ramsey number R(G 1 , G 2 , ..., G k ) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, there is always a monochromatic copy of G i colored with i, for some 1 ≤ i ≤ k. Let P k (resp. C k ) be the path (resp. cycle) on k vertices. In the paper we show that R(P 3 , C k , C k ) = R(C k , C k ) = 2k − 1 for odd k. In addition, we provide the exact values for Ramsey numbers R(P 4 , P 4 , C k ) = k + 2 and R(P 3 , P 5 , C k ) = k + 1.
The International Journal of Computers, Systems and Signal, 2002
Lecture Notes in Computer Science, 2002
This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to... more This paper investigates the complexity of scheduling biprocessor tasks on dedicated processors to minimize mean flow time. Since the general problem is strongly NP-hard, we assume some restrictions on task lengths and the structure of associated scheduling graphs. Of particular interest are acyclic graphs. In this way we identify a borderline between NP-hard and polynomially solvable special cases.
1999 7th IEEE International Conference on Emerging Technologies and Factory Automation. Proceedings ETFA '99 (Cat. No.99TH8467), 1999
... In this way we have UET sNPh [ 13 Bar-Noy A., Bellare M., Halld6rsson MM, Shachuai H., Tamir ... more ... In this way we have UET sNPh [ 13 Bar-Noy A., Bellare M., Halld6rsson MM, Shachuai H., Tamir T., On chromatic sums and distributed resourse allocation, Infor. and Comput. 140, 183-202 (1998). [2]Cai XQ, Lee CY, Li CL, Minimizing total completion time in two-processor task ...
For given graphs G 1 , G 2 , ..., G k , where k ≥ 2, the multicolor Ramsey number R(G 1 , G 2 , .... more For given graphs G 1 , G 2 , ..., G k , where k ≥ 2, the multicolor Ramsey number R(G 1 , G 2 , ..., G k ) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, there is always a monochromatic copy of G i colored with i, for some 1 ≤ i ≤ k. Let P k (resp. C k ) be the path (resp. cycle) on k vertices. In the paper we show that R(P 3 , C k , C k ) = R(C k , C k ) = 2k − 1 for odd k. In addition, we provide the exact values for Ramsey numbers R(P 4 , P 4 , C k ) = k + 2 and R(P 3 , P 5 , C k ) = k + 1.
In this paper we consider a problem of preemptive scheduling of multiprocessor tasks on dedicated... more In this paper we consider a problem of preemptive scheduling of multiprocessor tasks on dedicated processors in order to minimize the sum of completion times. Using the standard notation this problem is denoted as P|fix j , pmtn|ΣCj. We give a wide class of polynomial cases in terms of conflicting graphs.
Journal of Graph Theory, 1999
With the help of computer algorithms, we improve the lower bound on the edge Folkman number F e (... more With the help of computer algorithms, we improve the lower bound on the edge Folkman number F e (3, 3; 5) and vertex Folkman number F v (3, 3; 4), and thus show that the exact values of these numbers are 15 and 14, respectively. We also present computer enumeration of all critical graphs.
Discrete Mathematics, 1996
We consider the problem of efficient coloring of the edges of a so-called binomial tree T, i.e. a... more We consider the problem of efficient coloring of the edges of a so-called binomial tree T, i.e. acyclic graph containing two kinds of edges: those which must have a single color and those which are to be colored with L consecutive colors, where L is an arbitrary integer greater than 1. We give an O(n) time algorithm for optimal coloring
Discrete Mathematics, 1997
Discrete Mathematics, 2001
For a given approximate coloring algorithm a graph is said to be slightly hard-to-color (SHC) if ... more For a given approximate coloring algorithm a graph is said to be slightly hard-to-color (SHC) if some implementation of the algorithm uses more colors than the chromatic number. Similarly, a graph is said to be hard-to-color (HC) if every implementation of the algorithm results in a non-optimal coloring. In the paper, we study the smallest of such graphs for the DSATUR vertex coloring algorithm.
With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4... more With the help of computer algorithms, we improve the lower bound on the Ramsey multiplicity of K4, and thus show that the exact value of it is equal to 9. K 4 and K 4 − e. The value of M (K 4 − e) was later determined by Schwenk (cited in [2]). The upper bound M (K 4 ) ≤ 12 was given in 1980 by Jacobson [4], and in 1988 Exoo [1] improved it by 3. The only nontrivial lower bound M (K 4 ) ≥ 4 was recently presented by Olpp [7]. In this paper we improve this lower bound and thus show that M (K 4 ) = 9.
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Papers by Konrad Piwakowski