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Given a graph G = (V,E) with a set W ⊆ V of vertices, we enumerate colorings to W such that for every two enumerated colorings c and c' the corresponding colored graphs (G, c) and (G, c') are not isomorphic. This problem has an important application in the study of isomers of chemical graphs such as generation of benzen isomers from a tree-like chemical graph structure. The number of such colorings...
The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard optimization problems. Following a recent trend of research which focuses on developing algorithms for special types of TSP instances, namely graphs of limited degree, and thus alleviating a part of the time and space complexity, we present a polynomial-space branching algorithm for the TSP in graphs with degree at most 5,...
In this paper, we consider a combinatorial optimization problem of scheduling n jobs of block type on linearly aligned m identical machines. Each job Jj is characterized by four integers, an arrival time aj , a processing time pj, the number qj of consecutive machines required by the job (hence, each job Jj can be represented by a rectangular block with the size of pj × qj in a geometrical interpretation),...
In this paper, we consider the problem of computing a minimum k-partition of a finite set V with a set function f : 2V rarr Ropf, where the cost of a k-partition {V1, V2 ,..., Vk} is defined by Sigma1lesileskf(Vi). This problem contains the problem of partitioning a vertex set of an edge-weighted hypergraph into k components by removing the least cost of hyperedges. We show that, for a symmetric and...
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