# The maximum capacity shortest path problem : generation of efficient solution sets

T. Brian Boffey; R. C. Williams; B. Pelegrín; P. Fernandez

RAIRO - Operations Research - Recherche Opérationnelle (2002)

- Volume: 36, Issue: 1, page 1-19
- ISSN: 0399-0559

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topBoffey, T. Brian, et al. "The maximum capacity shortest path problem : generation of efficient solution sets." RAIRO - Operations Research - Recherche Opérationnelle 36.1 (2002): 1-19. <http://eudml.org/doc/245804>.

@article{Boffey2002,

abstract = {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 minimise 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.},

author = {Boffey, T. Brian, Williams, R. C., Pelegrín, B., Fernandez, P.},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {quickest path; shortest path; path capacity; efficient solution},

language = {eng},

number = {1},

pages = {1-19},

publisher = {EDP-Sciences},

title = {The maximum capacity shortest path problem : generation of efficient solution sets},

url = {http://eudml.org/doc/245804},

volume = {36},

year = {2002},

}

TY - JOUR

AU - Boffey, T. Brian

AU - Williams, R. C.

AU - Pelegrín, B.

AU - Fernandez, P.

TI - The maximum capacity shortest path problem : generation of efficient solution sets

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2002

PB - EDP-Sciences

VL - 36

IS - 1

SP - 1

EP - 19

AB - 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 minimise 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.

LA - eng

KW - quickest path; shortest path; path capacity; efficient solution

UR - http://eudml.org/doc/245804

ER -

## References

top- [1] T.B. Boffey, Multiobjective routing problems. TOP 3 (1995) 167-220. Zbl0852.90065MR1383800
- [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. Zbl1010.90517MR1799726
- [4] G.-H. Chen and Y.-C. Hung, On the quickest path problem. Inform. Process. Lett. 46 (1993) 125-128. Zbl0779.68065MR1229198
- [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. Zbl0795.90079
- [6] Y.L. Chen and Y.H. Chin, The quickest path problem. Comput. Oper. Res. 17 (1990) 179-188. Zbl0698.90083MR1035840
- [7] Y.L. Chen, An algorithm for finding the $k$ quickest paths in a network. Comput. Oper. Res. 20 (1993) 59-65. Zbl0773.90081MR1191985
- [8] Y.L. Chen, Finding the $k$ quickest simple paths in a network. Inform. Process. Lett. 50 (1994) 89-92. Zbl0804.90129MR1281046
- [9] J.L. Cohon, Multiobjective Programming and Planning. Academic Press (1978). Zbl0462.90054MR533667
- [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. Zbl0569.90062MR811082
- [11] J.S. Dai, S.N. Wang and X.Y. Yang, The multichannel quickest path problem. Int. J. Systems Sci. 25 (1994) 2047-2056. Zbl0818.90047MR1309604
- [12] E.V. Denardo and B.L. Fox, Shortest-route methods: 1. Reaching, pruning, and buckets. Oper. Res. 27 (1979) 161-186. Zbl0391.90089MR519570
- [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. Zbl0414.68035MR546998
- [14] E.W. Dijkstra, A note on two problems in connection with graphs. Numer. Maths 1 (1959) 269-271. Zbl0092.16002MR107609
- [15] M.L. Fredman and R.E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34 (1987) 596-615. MR904195
- [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). MR1229198
- [19] Y.-C. Hung and G.-H. Chen, Distributed algorithms for the quickest path problem. Parallel Comput. 18 (1992) 823-834. Zbl0754.68057MR1179813
- [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. Zbl0795.90079
- [21] Y.-C. Hung and G.-H. Chen, The quickest path problem in distributed computing systems. Springer, Lecture Notes in Comput. Sci. 579 (1992). MR1229514
- [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. MR1465222
- [23] D. Lee and E. Papadopolou, The all-pairs quickest path problem. Inform. Process. Lett. 45 (1993) 261-267. Zbl0768.68049MR1211538
- [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. MR439108
- [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. Zbl0234.90063MR309540
- [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. Zbl0642.90097MR835634
- [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. Zbl0747.90104MR1125875
- [30] R.E. Steuer, Multiple Criteria Optimization: Theory, Computation and Applications. Wiley (1986). Zbl0663.90085MR836977

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