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Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best… (More)

Branch and bound algorithms are general methods applied to various combinatorial optimization problems. Recently, parallelizations of these algorithms have been proposed. In spite of the generality of these methods, many of the parallelizations have been set up for a speciic problem and a speciic parallel computer. In this paper, a generalized utility PUBB… (More)

Branch-and-bound algorithms are general methods applicable to various combinatorial optimization problems and parallelization is one of the most hopeful methods to improve these algorithms. Parallel branch-and-bound algorithm implementations can be divided in two types based on whether a central or a distributed control scheme is used. Central control… (More)

Given an (undirected) graph G = V ; E ; a clique of G is a subset of vertices in which every pair is connected by an edge. The problem of finding a clique of maximum size is a classical NP–hard problem, and many algorithms, both heuristic and exact, have been proposed. While the philosophy behind the heuristic algorithms varies greatly, almost all of the… (More)

An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial… (More)