The Swap Edges of a Multiple-Sources Routing Tree

Authors:
Bang Ye Wu;Chih-Yuan Hsiao;Kun-Mao Chao
Affiliations:
Shu-Te University, Department of Computer Science and Information Engineering, YenChau, 824, Kaohsiung, Taiwan;National Taiwan University, Department of Computer Science and Information Engineering, YenChau, 106, Taipei, Taiwan;National Taiwan University, Department of Computer Science and Information Engineering/Graduate Institute of Networking and Multimedia, YenChau, 106, Taipei, Taiwan
Venue:
Algorithmica
Year:
2008

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ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Brief Annoucement: Distributed Swap Edges Computation for Minimum Routing Cost Spanning Trees

OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Finding best swap edges minimizing the routing cost of a spanning tree

MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science

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Abstract

Let T be a spanning tree of a graph G and S⊂V(G) be a set of sources. The routing cost of T is the total distance from all sources to all vertices. For an edge e of T, the swap edge of e is the edge f minimizing the routing cost of the tree formed by replacing e with f. Given an undirected graph G and a spanning tree T of G, we investigate the problem of finding the swap edge for every tree edge. In this paper, we propose an O(mlog n+n2)-time algorithm for the case of two sources and an O(mn)-time algorithm for the case of more than two sources, where m and n are the numbers of edges and vertices of G, respectively.