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Series-parallel Graph (series-parallel + graph)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 6 2002
S. Raghavan
Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph,a directed series-parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series-parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574,592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031 [source]

Low-connectivity network design on series-parallel graphs

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 3 2004
S. Raghavan
Abstract Network survivability is a critical issue for modern fiber-optic telecommunication networks. Networks with alternate routes between pairs of nodes permit users to communicate in the face of equipment failure. In this paper, we consider the following low-connectivity network design (LCND) problem: Given a graph G = (N, E) and a connectivity requirement di , {0, 1, 2} for each node and edge costs ce for each edge e , E, design a minimum-cost network that contains at least dst = min{ds, dt} disjoint paths between nodes s and t. We present linear-time algorithms for both node- and edge-connectivity versions of the problem on series-parallel graphs. Due to the sparsity of telecommunications networks, this algorithm can be applied to obtain partial solutions and decompositions that may be embedded in a heuristic solution procedure as well as exact solution algorithms for the problem on general graphs. © 2004 Wiley Periodicals, Inc. [source]