作者：
ASANO, TUNIV TOKYO
FAC ENGN DEPT MATH ENGN & INSTRUMENTAT PHYS BUNKYO KU TOKYO 113 JAPAN
For a property π\pi on graphs, the corresponding edge-deletion problem PED(π)P_{{\text{ED}}} (\pi ) (on planar graphs) is stated as follows: given a (planar) graph G, find a set of edges of minimum cardinality whos...
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The optimum communication spanning tree problem is to locate a spanning tree which minimizes the sum of the lengths of the shortest routes between all pairs of vertices in a graph, weighted by traffic requirements. Al...
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The optimum communication spanning tree problem is to locate a spanning tree which minimizes the sum of the lengths of the shortest routes between all pairs of vertices in a graph, weighted by traffic requirements. Although NP-complete in general, this problem has an efficient solution for series-parallel graphs when all requirements are equal. This problem was introduced by Hu, who gave an efficient solution for the restricted case when the network is complete and the distances are equal.
Given a graphG = (N, E) and a length functionl: E → ?, the graphical Traveling Salesman Problem is that of finding a minimum length cycle goingat least once through each node ofG. This formulation has advantages over...
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Given a graphG = (N, E) and a length functionl: E → ?, the graphical Traveling Salesman Problem is that of finding a minimum length cycle goingat least once through each node ofG. This formulation has advantages over the traditional formulation where each node must be visited exactly once. We give some facet inducing inequalities of the convex hull of the solutions to that problem. In particular, the so-called comb inequalities of Gr?tschel and Padberg are generalized. Some related integer polyhedra are also investigated. Finally, an efficient algorithm is given whenG is a series-parallel graph.
A series-parallel graph can be constructed from a certain graph by recurslvely applying “series” and “parallel” connections The class of such graphs, which Is a well-known model of series-parallel electrical netwo...
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Given a set ofn events (or jobs) which are constrained by a precedence relation, we want to order them into a totally ordered sequence (i. e., one machine schedule). Each event has an integer cost (which may be negati...
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Given a set ofn events (or jobs) which are constrained by a precedence relation, we want to order them into a totally ordered sequence (i. e., one machine schedule). Each event has an integer cost (which may be negative) associated with it, and our objective is to minimize the maximum cumulative cost within a schedule, i. e., to obtain a cumulative cost-optimal schedule. We introduce the concept of “strict optimality” and investigate properties of strictly optimal schedules. The usefulness of these schedules is demonstrated in the special case where the precedence relation is “series-parallel”. For this case we describe an algorithm which finds a cumulative cost-optimal schedule inO (n logn) time.
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