Filtry
wszystkich: 156
Wyniki wyszukiwania dla: polynomial algorithm.
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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublikacjaDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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A polynomial algorithm for finding T-span of generalized cacti
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A polynomial algorithm for finding T-span of generalized cacti.
PublikacjaW pracy opisano wielomianowy algorytm wyznaczający optymalne T-pokolorowania dla uogólnionych kaktusów.
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A polynomial algorithm for solving a general max‐min fairness problem
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A polynomial algorithm for some preemptive multiprocessor task scheduling problems.
Publikacja.
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A note on polynomial algorithm for cost coloring of bipartite graphs with Δ ≤ 4
PublikacjaIn the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree ∆≤4 can be solved in O(n^2) time. This extends Jansen’s result [K.Jansen,The optimum cost chromatic partition problem, in:...
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A self-stabilizing algorithm for finding a spanning tree in a polynomial number of moves
PublikacjaW pracy rozważa się rozproszony model obliczeń, w którym struktura systemu jest reprezentowana przez graf bezpośrednich połączeń komunikacyjnych. W tym modelu podajemy nowy samostabilizujący algorytm znajdowania drzewa spinającego. Zgodnie z naszą wiedzą jest to pierwszy algorytm dla tego problemu z gwarantowaną wielomianową liczbą ruchów.
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ANYTIME POLYNOMIAL HEURISTIC ALGORITHM FOR PARTITIONING GROUPS OF DATA WITH PRESERVING CLASS PROPORTIONS FOR CROSS-VALIDATION
PublikacjaThe article describes a problem of splitting data for k-fold cross-validation, where class proportions must be preserved, with additional constraint that data is divided into groups that cannot be split into different cross-validation sets. This problem often occurs in e.g. medical data processing, where data samples from one patient must be included in the same cross-validation set. As this problem is NP-complete, a heuristic...
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Better polynomial algorithms for scheduling unit-length jobs with bipartite incompatibility graphs on uniform machines
PublikacjaThe goal of this paper is to explore and to provide tools for the investigation of the problems of unit-length scheduling of incompatible jobs on uniform machines. We present two new algorithms that are a significant improvement over the known algorithms. The first one is Algorithm 2 which is 2-approximate for the problem Qm|p j = 1, G = bisubquartic|Cmax . The second one is Algorithm 3 which is 4-approximate for the problem Qm|p...
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Implementation of discrete convolution using polynomial residue representation
PublikacjaConvolution is one of the main algorithms performed in the digital signal processing. The algorithm is similar to polynomial multiplication and very intensive computationally. This paper presents a new convolution algorithm based on the Polynomial Residue Number System (PRNS). The use of the PRNS allows to decompose the computation problem and thereby reduce the number of multiplications. The algorithm has been implemented in Xilinx...
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Discrete convolution based on polynomial residue representation
PublikacjaThis paper presents the study of fast discrete convolution calculation with use of the Polynomial Residue Number System (PRNS). Convolution can be based the algorithm similar to polynomial multiplication. The residue arithmetic allows for fast realization of multiplication and addition, which are the most important arithmetic operations in the implementation of convolution. The practical aspects of hardware realization of PRNS...
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublikacjaWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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Scheduling on Uniform and Unrelated Machines with Bipartite Incompatibility Graphs
PublikacjaThe problem of scheduling jobs on parallel machines under an incompatibility relation is considered in this paper. In this model, a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same machine. We consider job scheduling under the incompatibility relation modeled by a bipartite graph, under the makespan optimality criterion, on uniform and unrelated machines. Unrelated machines...
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Shared processor scheduling
PublikacjaWe study the shared processor scheduling problem with a single shared processor to maximize total weighted overlap, where an overlap for a job is the amount of time it is processed on its private and shared processor in parallel. A polynomial-time optimization algorithm has been given for the problem with equal weights in the literature. This paper extends that result by showing an (log)-time optimization algorithm for a class...
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On the Characteristic Graph of a Discrete Symmetric Channel
PublikacjaWe present some characterizations of characteristic graphs of row and/or column symmetric channels. We also give a polynomial-time algorithm that decides whether there exists a discrete symmetric channel whose characteristic graph is equal to a given input graph. In addition, we show several applications of our results.
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Scheduling of unit-length jobs with bipartite incompatibility graphs on four uniform machines
PublikacjaThe problem of scheduling n identical jobs on 4 uniform machines with speeds s1>=s2>=s3>=s4 is considered.The aim is to find a schedule with minimum possible length. We assume that jobs are subject to mutual exclusion constraints modeled by a bipartite incompatibility graph of degree delta. We show that the general problem is NP-hard even if s1=s2=s3. If, however, delta<5 and s1>12s2 s2=s3=s4, then the problem can be solved to...
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On Computational Aspects of Greedy Partitioning of Graphs
PublikacjaIn this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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Equitable coloring of hypergraphs
PublikacjaA hypergraph is equitablyk-colorable if its vertices can be partitioned into k sets/colorclasses in such a way that monochromatic edges are avoided and the number of verticesin any two color classes differs by at most one. We prove that the problem of equitable 2-coloring of hypergraphs is NP-complete even for 3-uniform hyperstars. Finally, we apply the method of dynamic programming for designing a polynomial-time algorithm to...
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Modeling and analysis of the effectiveness of the guard systemswith dynamic graphs
PublikacjaIn the following paper it will be presented a new model for analysis (in polynomial time) of the effectiveness of the guard systems. Therewill be presented its practical applications in problems such as searching for the weakest points of the system, planning guards' paths or cameras deployment, switching image from multiple cameras on several monitors, or interception of the intruder. This model is based on describing the guarded...
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Computational aspects of greedy partitioning of graphs
PublikacjaIn this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...