Node weighted network upgrade problems

Conference · Sun Sep 01 04:00:00 EDT 1996

OSTI ID:373929

Krumke, S O; Noltemeier, H ^[1]; Marathe, M V ^[2]; Ravi, S S ^[3]

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1. Univ. of Wuerzburg (Germany). Dept. of Computer Science
2. Los Alamos National Lab., NM (United States)
3. State Univ. of New York, Albany, NY (United States). Dept. of Computer Science

Consider a network where nodes represent processors and edges represent bidirectional communication links. The processor at a node v can be upgraded at an expense of cost(v). Such an upgrade reduces the delay of each link emanating from v by a fixed factor x, where 0 < x < 1. The goal is to find a minimum cost set of nodes to be upgraded so that the resulting network has a spanning tree in which edge is of delay at most a given value {delta}. The authors provide both hardness and approximation results for the problem. They show that the problem is NP-hard and cannot be approximated within any factor {beta} < ln n, unless NP {improper_subset} DTIME(n{sup log log n}), where n is the number of nodes in the network. They then present the first polynomial time approximation algorithms for the problem. For the general case, the approximation algorithm comes within a factor of 2 ln n of the minimum upgrading cost. When the cost of upgrading each node is 1, they present an approximation algorithm with a performance guarantee of 4(2 + ln {Delta}), where {Delta} is the maximum node degree. Finally, they present a polynomial time algorithm for the class of treewidth-bounded graphs.

• Research Organization: Los Alamos National Lab., NM (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 373929
• Report Number(s): LA-UR--96-1467; CONF-961004--2; ON: DE96011233
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPUTER NETWORKS
DATA TRANSMISSION
DIAGRAMS
MATHEMATICS
MODIFICATIONS
PERFORMANCE