TY - JOUR

T1 - Algorithms for the quickest path problem and the enumeration of quickest paths

AU - Rosen, J. B.

AU - Sun, S. Z.

AU - Xue, G. L.

N1 - Funding Information:
*This research was supported in part by the Air Force Office of Scientific Research grant AFOSR-879127, the National Science Foundation grant DCR-8420935 and a University of Minnesota Graduate School Doctoral Dissertation Fellowship. The authors of this paper are listed in alphabetical order. M. B. Rosen is a Professor of Computer Science at the Unive~ity of Minnesota. His research interests include large-scale numerical optimi~tion, global optimi~tion, and parallel imputing. He has published over IOOt echnical papers, is an editor of two journals and is the author or editor of 5 books. $.-Z. Sun is a Ph.D. student in the Computer Science Department, University of Minnesota. His research interests include combinatorial optimization and parallel computing. He has previously published in the JournaIqf’Shunc/oy/ Univmity. $G.-L. Xue is a Ph.D student in the Computer Science Department. University of Minnesota. He is also from the Institute ol Operations Research, Qufu Normal University. His research interests lie in the design and implementation of sequential and parallel algorithms for optimization problems. He has published papers in Opcruricurs Remwh, ORSA Jmmtai ttn C~:nfpuli~#C, oniputer.s& Operuf&ns Respurdt. JOTA and others. CAll correspondence should be addressed to: Dr G.-L. Xue, Computer Science Department, University of Minnesota, Minneapolis, MN 55455. U.S.A.

PY - 1991

Y1 - 1991

N2 - Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = |V|, e = |A|, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn2 log n).

AB - Let N = (V, A, c, l) be an input network with node set V, arc set A, positive arc weight function c and nonnegative arc weight function l. Let σ be the amount of data to be transmitted. The quickest path problem is to find a routing path in N to transmit the given amount of data in minimum time. In a recent paper, Chen and Chin proposed this problem and developed algorithms for the single pair quickest path problem with time complexity O(re + rn log n), where n = |V|, e = |A|, and r is the number of distinct capacity values of N. In this paper, we first develop an alternative algorithm for the single pair quickest path problem with same time complexity and less space requirement. We then study the constrained quickest path problem and propose an O(re + rn log n) time algorithm. Finally, we develop an algorithm to enumerate the first m quickest paths to send a given amount of data from one node to another with time complexity O(rmne + rmn2 log n).

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U2 - 10.1016/0305-0548(91)90063-W

DO - 10.1016/0305-0548(91)90063-W

M3 - Article

AN - SCOPUS:0025862824

VL - 18

SP - 579

EP - 584

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

IS - 6

ER -