Scalable parallel algorithms for difficult combinatorial problems: A case study in optimization

A novel combination of emergent algorithmic methods, powerful computational platforms and supporting infrastructure is described. These complementary tools and technologies are used to launch systematic attacks on combinatorial problems of significance. As a case study, optimal solutions to very large instances of the NP-hard vertex cover problem are computed. To accomplish this, an efficient sequential algorithm and two forms of parallel algorithms are devised and implemented. The importance of maintaining a balanced decomposition of the search space is shown to be critical to achieving scalability. With the synergistic combination of techniques detailed here, it is now possible to solve problem instances that before were widely viewed as hopelessly out of reach. Target problems need only be amenable to reduction and decomposition. Applications are also discussed.

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