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Abstract. We show that any k-connected graph G = (V, E) has a sparse k-connected spanning subgraph G'= (V, E') with IE'I = O(kl VI) by presenting an O(IEL)-time algorithm to find one such subgraph, where connectivity stands for either edge-connectivity or node-connectivity. By using this algorithm as preprocessing, the time complexities of some graph problems related to connectivity can be improved. For example, the current best time bound O(max{k21VI 1/2, k l V I}IEI) to determine whether node-connectivity x(G) of a graph G = (V, E) is larger than a given integer k or not can be reduced to O(max{k31Vp/2, k21VI2}).

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We discuss an integer programming formulation for a class of cooperative games. We focus on algorithmic aspects of the core, one of the most important solution concepts in cooperative game theory. Central to our study is a simple (but very useful) observation that the core for this class is nonempty if and only if an associated linear program has an integer optimal solution. Based on this, we study the computational complexity and algorithms to answer important questions about the cores of various games on graphs, such as maximum flow, connectivity, maximum matching, minimum vertex cover, minimum edge cover, maximum independent set, and minimum coloring.

This paper investigates the use of Boolean techniques in a systematic study of cause-effect relationships. The model uses partially defined Boolean functions. Procedures are provided to extrapolate from limited observations, concise and meaningful theories to explain the effect under study, and to prevent (or provoke) its occurrence.

This article gives an efficient algorithm for obtaining K shortest simple paths between two specified nodes in an undirected graph G with non-negative edge lengths. Letting n be the number of nodes and m be the number of edges in G, its running time is

Using the nested loops method, this paper addresses the problem of minimizing the number of page fetches necessary to evaluate a given query to a relational database. We first propose a data structure whereby the number of page fetches required for query evaluation is substantially reduced and then derive a formula for the expected number of page fetches. An optimal solution to our problem is the nesting order of relations in the evaluation program, which minimizes the number of page fetches. Since the minimization of the formula is NP-hard, as shown in the Appendix, we propose a heuristic algorithm which produces a good suboptimal solution in polynomial time. For the special case where the input query is a “tree query,” we present an efficient algorithm for finding an optimal nesting order.

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