A New Approach to Cactus Construction Applied to TSP Support Graphs
We present a novel approach to the construction of the cactus representation of all minimum cuts of a graph. The representation is a supergraph that stores the set of all mincuts compactly and mirrors its structure. We focus on support graphs occurring in the branch-and-cut approach to traveling salesman, vehicle routing and similar problems in a natural way. The ideas presented also apply to more general graphs. Unlike most previous construction approaches, we do not follow the Karzanov-Timofeev framework or a variation of it. Our deterministic algorithm is based on inclusion-minimal mincuts. We use Fleischer’s approach [J. Algorithms, 33(1):51–72, 1999], one of the fastest to date, as benchmark. The new algorithm shows an average speed-up factor of 20 for TSP-related support graphs in practice. We report computational results. Compared to the benchmark, we reduce the space required during construction for n-vertex graphs with m edges from Open image in new window to Open image in new window .
KeywordsTravel Salesman Problem Weighted Graph Tree Edge Capacitate Vehicle Route Problem Support Graph
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