d-separated paths in hypercubes and star graphs

In this paper, we consider a generalized node disjoint paths problem: d-separated paths problem. In a graph G, given two distinct nodes s and t, two paths P and Q, connecting s and t, are d-separated if d/sub G-{s,t}//spl ges/d for any u/spl isin/P-{s,t} and v/spl isin/Q-{s,t}, where d/sub G-{s,t}/(...

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Veröffentlicht in:Proceedings of 1996 IEEE Second International Conference on Algorithms & Architectures for Parallel Processing, ICA³PP '96 : June 11-13, 1996, Singapore S. 340 - 347
Hauptverfasser: Qian-Ping Gu, Shietung Peng
Format: Tagungsbericht
Sprache:Englisch
Japanisch
Veröffentlicht: IEEE 24.12.2002
Schlagworte:
Distributed computing
Fault tolerance
Hypercubes
Joining processes
Multiprocessor interconnection networks
Routing
Software
ISBN:9780780335295, 0780335295
Online-Zugang:Volltext
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Zusammenfassung:In this paper, we consider a generalized node disjoint paths problem: d-separated paths problem. In a graph G, given two distinct nodes s and t, two paths P and Q, connecting s and t, are d-separated if d/sub G-{s,t}//spl ges/d for any u/spl isin/P-{s,t} and v/spl isin/Q-{s,t}, where d/sub G-{s,t}/(u,v) is the distance between u and v in the reduced graph G-{s,t}. d-separated paths problem is to find as many d-separated paths between s and t as possible. In this paper, we give the following results on d-separated paths problems on n-dimensional hypercubes H/sub n/ and star graphs G/sub n/. Given s and t in H/sub n/, there are at least (n-2) 2-separated paths between s and t. (n-2) is the maximum number of 2-separated paths between s and t for d(s,t)/spl ges/4. Moreover, (n-2) and separated paths of length at most d(s,t)+2 for d(s,t)<n and of length n for d(s,t)=n between s and t can be constructed in O(n/sup 2/) optimal line. For d/spl ges/3, d-separated paths in H/sub n/ do not exist. Given s and t in G/sub n/, there are exactly (n-1) d-separated paths between s and t for 1/spl les/d/spl les/3 (n-1) 3-separated paths of length at most min{d(s,t)+4, d(G/sub n/)+2} between s and t can be constructed in O(n/sup 2/) optimal time, where d(G/sub n/)=[3(n-1)/2]. For d/spl ges/5 d-separated paths in G/sub n/ do not exist.
ISBN:9780780335295
0780335295
DOI:10.1109/ICAPP.1996.562894