Finding minimum hybrid cost core on weighted tree networks

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:471987

Yang, Shin-Jer ^[1]

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1. Soochow Univ., Taipei (Taiwan, Province of China)

This paper addresses a network problem on weighted tree networks, which we want to find a core with the minimum building cost under some distance measures, called the hybrid cost core problem. Let G(V, E) denote a network in which each node v {element_of} V is associated with a positive cost C(v) and each link e {element_of} E is associated with a positive length L (e). There are clients at the nodes who request services. We want to allocate a set of servers at some nodes to provide the services to the clients. A client at a node x needs to move to any one node with server if there is no server at that node. We assume that the services provided by each server are identical, but the costs are different for building them at different nodes. So, for each node v, C(v) represents the cost to build a server at v and each link e = (u,v), W(e) represents the distance between u and v. Given a core P = (p{sub 1}, ..., p{sub s}) of G, we denote the distance between P and the clients at a node x with no server to be d(x, P). The d(x, P) is defined to be min{sub 1}{le}j{le}s(d(x, p{sub j})), where d(x, p{sub j}) denotes the length of the shortest path from x to p{sub j}. Meanwhile, we propose two types of distance measures for a core: the min-max distance and the min-average distance. We first show some properties of optimal solutions for these two types of measures. Then, we give linear time algorithms for finding the cores with the minimum hybrid cost under these two measures on weighted tree networks by the dynamic programming strategy. The generalization of our results to p-cores are also discussed. The core problems that we consider are more general than the typical one.

• OSTI ID: 471987
• Report Number(s): CONF-960220--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
DYNAMIC PROGRAMMING
NETWORK ANALYSIS
OPTIMIZATION