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The maximum capacity shortest path problem: Generation of efficient solution sets. (English) Zbl 1006.90013

Summary: Individual items of flow in a telecommunications or a transportation network may need to be separated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destination will depend on the size of the convoy. The quickest path problem seeks a path to minimize this convoy travel time. A closely related bicriterion problem is the maximum capacity shortest path problem. For this latter problem, an effective implementation is devised for an algorithm to determine desired sets of efficient solutions which in turn facilitates the search for a “best” compromise solution. Numerical experience with the algorithm is reported.

MSC:

90B10 Deterministic network models in operations research
90B18 Communication networks in operations research
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[1] T.B. Boffey , Multiobjective routing problems . TOP 3 ( 1995 ) 167 - 220 . MR 1383800 | Zbl 0852.90065 · Zbl 0852.90065 · doi:10.1007/BF02568585
[2] T.B. Boffey , Distributed Computing: associated combinatorial problems . McGraw-Hill ( 1992 ).
[3] T.B. Boffey , Efficient solution generation for the Bicriterion Routing problem . Belg. J. Oper. Res. Statist. Comput. Sci. 39 ( 2000 ) 3 - 20 . MR 1799726 | Zbl 1010.90517 · Zbl 1010.90517
[4] G.-H. Chen and Y.-C. Hung , On the quickest path problem . Inform. Process. Lett. 46 ( 1993 ) 125 - 128 . MR 1229198 | Zbl 0779.68065 · Zbl 0779.68065 · doi:10.1016/0020-0190(93)90057-G
[5] G.-H. Chen and Y.-C. Hung , Algorithms for the constrained quickest path problem and the enumeration of quickest paths . Comput. Oper. Res. 21 ( 1994 ) 113 - 118 . Zbl 0795.90079 · Zbl 0795.90079 · doi:10.1016/0305-0548(94)90045-0
[6] Y.L. Chen and Y.H. Chin , The quickest path problem . Comput. Oper. Res. 17 ( 1990 ) 179 - 188 . MR 1035840 | Zbl 0698.90083 · Zbl 0698.90083 · doi:10.1016/0305-0548(90)90039-A
[7] Y.L. Chen , An algorithm for finding the \(k\) quickest paths in a network . Comput. Oper. Res. 20 ( 1993 ) 59 - 65 . MR 1191985 | Zbl 0773.90081 · Zbl 0773.90081 · doi:10.1016/0305-0548(93)90096-2
[8] Y.L. Chen , Finding the \(k\) quickest simple paths in a network . Inform. Process. Lett. 50 ( 1994 ) 89 - 92 . MR 1281046 | Zbl 0804.90129 · Zbl 0804.90129 · doi:10.1016/0020-0190(94)00008-5
[9] J.L. Cohon , Multiobjective Programming and Planning . Academic Press ( 1978 ). MR 533667 | Zbl 0462.90054 · Zbl 0462.90054
[10] J.R. Current , C.S. ReVelle and J.L. Cohon , The maximum covering/shortest path problem: A multiobjective network design and routing problem . EJOR 21 ( 1985 ) 189 - 199 . MR 811082 | Zbl 0569.90062 · Zbl 0569.90062 · doi:10.1016/0377-2217(85)90030-X
[11] J.S. Dai , S.N. Wang and X.Y. Yang , The multichannel quickest path problem . Int. J. Systems Sci. 25 ( 1994 ) 2047 - 2056 . MR 1309604 | Zbl 0818.90047 · Zbl 0818.90047 · doi:10.1080/00207729408949334
[12] E.V. Denardo and B.L. Fox , Shortest-route methods: 1 . Reaching, pruning, and buckets. Oper. Res. 27 ( 1979 ) 161 - 186 . MR 519570 | Zbl 0391.90089 · Zbl 0391.90089 · doi:10.1287/opre.27.1.161
[13] R. Dial , F. Glover , D. Karney and D. Klingman , A computational analysis of alternative algorithms and labelling techniques for finding shortest path trees . Networks 9 ( 1974 ) 215 - 248 . MR 546998 | Zbl 0414.68035 · Zbl 0414.68035 · doi:10.1002/net.3230090304
[14] E.W. Dijkstra , A note on two problems in connection with graphs . Numer. Maths 1 ( 1959 ) 269 - 271 . Article | MR 107609 | Zbl 0092.16002 · Zbl 0092.16002 · doi:10.1007/BF01386390
[15] M.L. Fredman and R.E. Tarjan , Fibonacci heaps and their uses in improved network optimization algorithms . J. ACM 34 ( 1987 ) 596 - 615 . MR 904195
[16] P. Hart , N. Nilsson and B. Raphael , A formal basis for the heuristic determination of minimal cost paths . IEEE Trans Syst. Man. Cybernet. 4 ( 1968 ) 100 - 107 .
[17] Y.-C. Hung , Distributed algorithms for the constrained routing problem in computer networks . Computer Communications 21 ( 1998 ) 1476 - 1485 .
[18] Y.-C. Hung and G.-H. Chen , On the quickest path problem . Springer, Lecture Notes in Comput. Sci. 46 ( 1991 ). MR 1229198
[19] Y.-C. Hung and G.-H. Chen , Distributed algorithms for the quickest path problem . Parallel Comput. 18 ( 1992 ) 823 - 834 . MR 1179813 | Zbl 0754.68057 · Zbl 0754.68057 · doi:10.1016/0167-8191(92)90048-C
[20] Y.-C. Hung and G.-H. Chen , Algorithms for the constrained quickest path problem and the enumeration of quickest paths . Comput. Oper. Res. 21 ( 1994 ) 113 - 118 . Zbl 0795.90079 · Zbl 0795.90079 · doi:10.1016/0305-0548(94)90045-0
[21] Y.-C. Hung and G.-H. Chen , The quickest path problem in distributed computing systems . Springer, Lecture Notes in Comput. Sci. 579 ( 1992 ). MR 1229514
[22] D. Kagaris , G.E. Pantziou , S. Tragoudis and C.D. Zaroliagis , On the computation of fast data transmission in networks with capacities and delays . Springer, New York, Lecture Notes in Comput. Sci. 955 ( 1995 ) 291 - 302 . MR 1465222
[23] D. Lee and E. Papadopolou , The all-pairs quickest path problem . Inform. Process. Lett. 45 ( 1993 ) 261 - 267 . MR 1211538 | Zbl 0768.68049 · Zbl 0768.68049 · doi:10.1016/0020-0190(93)90214-T
[24] W.E. Leland , M.S. Taqqu , W. Willinger and D.V. Wilson , On the self-similar nature of Ethernet traffic . IEEE/ACM Trans. Networking 2 ( 1994 ) 1 - 15 .
[25] M.H. Moore , On the fastest route for convoy-type traffic in flowrate-constrained networks . Transportation Sci. 10 ( 1976 ) 113 - 124 . MR 439108
[26] G.L. Nemhauser , A generalized permanent label setting algorithm for the shortest path between specified nodes . J. Math. Anal. Appl. 38 ( 1972 ) 328 - 334 . MR 309540 | Zbl 0234.90063 · Zbl 0234.90063 · doi:10.1016/0022-247X(72)90091-1
[27] V. Paxson and S. Floyd , Wide-area traffic: The failure of Poisson modelling . Proc. ACM Sigcomm ’ 94 ( 1995 ) 149 - 160 .
[28] A. Perko , Implementation of algorithms for \(k\) shortest loopless paths . Networks 16 ( 1987 ) 149 - 160 . MR 835634 | Zbl 0642.90097 · Zbl 0642.90097 · doi:10.1002/net.3230160204
[29] J.B. Rosen , S.-Z. Sun and G.-L. Xue , Algorithms for the quickest path problem and the enumeration of quickest paths . Comput. Oper. Res. 18 ( 1991 ) 579 - 584 . MR 1125875 | Zbl 0747.90104 · Zbl 0747.90104 · doi:10.1016/0305-0548(91)90063-W
[30] R.E. Steuer , Multiple Criteria Optimization: Theory , Computation and Applications. Wiley ( 1986 ). MR 836977 | Zbl 0663.90085 · Zbl 0663.90085
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