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81.
An ant-based algorithm for coloring graphs 总被引:1,自引:0,他引:1
This paper presents an ant-based algorithm for the graph coloring problem. An important difference that distinguishes this algorithm from previous ant algorithms is the manner in which ants are used in the algorithm. Unlike previous ant algorithms where each ant colors the entire graph, each ant in this algorithm colors just a portion of the graph using only local information. These individual coloring actions by the ants form a coloring of the graph. Even with the lack of pheromone laying capacity by the ants, the algorithm performed well on a set of 119 benchmark graphs. Furthermore, the algorithm produced very consistent results, having very small standard deviations over 50 runs of each graph tested. 相似文献
82.
Disjoint triangles and quadrilaterals in a graph 总被引:1,自引:0,他引:1
Jin Yan 《Discrete Mathematics》2008,308(17):3930-3937
Let G be a simple graph of order n and s and k be two positive integers. Brandt et al. obtained the following result: If s?k, n?3s+4(k-s) and σ2(G)?n+s, then G contains k disjoint cycles C1,…,Ck satisfying |Ci|=3 for 1?i?s and |Ci|?4 for s<i?k. In the above result, the length of Ci is not specified for s<i?k. We get a result specifying the length of Ci for each s<i?k if n?3s+4(k-s)+3. 相似文献
83.
84.
We consider the question of characterizing Pfaffian graphs. We exhibit an infinite family of non-Pfaffian graphs minimal with respect to the matching minor relation. This is in sharp contrast with the bipartite case, as Little [C.H.C. Little, A characterization of convertible (0,1)-matrices, J. Combin. Theory Ser. B 18 (1975) 187–208] proved that every bipartite non-Pfaffian graph contains a matching minor isomorphic to K3,3. We relax the notion of a matching minor and conjecture that there are only finitely many (perhaps as few as two) non-Pfaffian graphs minimal with respect to this notion.We define Pfaffian factor-critical graphs and study them in the second part of the paper. They seem to be of interest as the number of near perfect matchings in a Pfaffian factor-critical graph can be computed in polynomial time. We give a polynomial time recognition algorithm for this class of graphs and characterize non-Pfaffian factor-critical graphs in terms of forbidden central subgraphs. 相似文献
85.
Quantum annealing extends simulated annealing by introducing artificial quantum fluctuations. The path-integral Monte Carlo version chosen is population-based and designed to be implemented on a classical computer. Its first application to the graph coloring problem is presented in this paper. It is shown by experiments that quantum annealing can outperform classical thermal simulated annealing for this particular problem. Moreover, quantum annealing proved competitive when compared with the best algorithms on most of the difficult instances from the DIMACS benchmarks. The quantum annealing algorithm has even found that the well-known benchmark graph dsjc1000.9 has a chromatic number of at most 222. This is an improvement on its best upper-bound from a large body of literature. 相似文献
86.
The current air traffic system is forecasted to face strong challenges due to the continuous increase in air traffic demand. Hence, there is a need for new types of organization permitting a more efficient air traffic management, with both a high capacity and a high level of safety, and possibly with a reduced environmental impact. In this article, we study a holistic approach, consisting in designing across Europe a very organized air traffic system, as opposed to free flight, to reduce costs while maintaining safety. 相似文献
87.
In economics, homothetic functions are production functions whose marginal technical rate of substitution is homogeneous of degree zero. Mathematically, a homothetic function is a function of the form f(x)=F(h(x1,…,xn)), where F is a monotonically increasing function and h is a homogeneous function of any degree d≠0. In this paper, we classify homothetic functions satisfying the homogeneous Monge–Ampère equation. Several applications to production models in economics will also be given. 相似文献
88.
《Operations Research Letters》2014,42(3):222-225
We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution is a subset of the input data. We introduce the notion of intersective approximability that generalizes the one of safe approximability introduced in Guo et al. (2011) and show strong parameterized inapproximability results for many of the subset problems handled. 相似文献
89.
90.
We give a competitive algorithm to identify all d defective edges in a hypergraph with d unknown. Damaschke did the d=1 case for 2-graphs, Triesch extended the d=1 case to r-graphs, and Johann did the general d case for 2-graphs. So ours is the first attempt to solve the searching for defective edges problem in its full generality. Further, all the above three papers assumed d known. We give a competitive algorithm where d is unknown. 相似文献