Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems

Given a network and a set of connection requests on it, we consider the maximum edge-disjoint paths and related generalizations and routing problems that arise in assigning paths for these requests. We present improved approximation algorithms and/or integrality gaps for all problems considered; the central theme of this work is the underlying multicommodity flow relaxation. Applications of these techniques to approximating families of packing integer programs are also presented.

[1]  Alok Aggarwal,et al.  Efficient routing in optical networks , 1996, JACM.

[2]  Yuval Rabani,et al.  On-line admission control and circuit routing for high performance computing and communication , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[3]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[4]  Aravind Srinivasan,et al.  Improved approximations of packing and covering problems , 1995, STOC '95.

[5]  Alan M. Frieze,et al.  Existence and construction of edge disjoint paths on expander graphs , 1992, STOC '92.

[6]  Joel H. Spencer,et al.  A useful elementary correlation inequality , 1989, J. Comb. Theory, Ser. A.

[7]  Richard Cole,et al.  Routing on butterfly networks with random faults , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[8]  Venkatesan Guruswami,et al.  Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems , 1999, STOC '99.

[9]  Bruce M. Maggs,et al.  Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules , 1999, Comb..

[10]  Yuval Rabani,et al.  Improved bounds for all optical routing , 1995, SODA '95.

[11]  Eli Upfal,et al.  An O(log N) deterministic packet-routing scheme , 1992, JACM.

[12]  C. Fortuin,et al.  Correlation inequalities on some partially ordered sets , 1971 .

[13]  Alan M. Frieze,et al.  Existence and Construction of Edge-Disjoint Paths on Expander Graphs , 1994, SIAM J. Comput..

[14]  Prabhakar Raghavan Randomized Approximation Algorithms in Combinatorial Optimization , 1994, FSTTCS.

[15]  Frank Thomson Leighton,et al.  An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[16]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[17]  Shekhar Y. Borkar,et al.  iWarp: an integrated solution to high-speed parallel computing , 1988, Proceedings. SUPERCOMPUTING '88.

[18]  Ronitt Rubinfeld,et al.  Short paths in expander graphs , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[19]  J. Vitter,et al.  Approximations with Minimum Packing Constraint Violation , 1992 .

[20]  Bruce M. Maggs,et al.  On-Line Algorithms for Path Selection in a Nonblocking Network , 1996, SIAM J. Comput..

[21]  Michael D. Noakes,et al.  The J-machine multicomputer: an architectural evaluation , 1993, ISCA '93.

[22]  J. Spencer Ten lectures on the probabilistic method , 1987 .

[23]  Frank Thomson Leighton Introduction to parallel algorithms and architectures: arrays , 1992 .

[24]  Éva Tardos,et al.  Approximations for the disjoint paths problem in high-diameter planar networks , 1995, STOC '95.

[25]  Richard M. Karp,et al.  On the Computational Complexity of Combinatorial Problems , 1975, Networks.

[26]  Yuval Rabani,et al.  Path coloring on the mesh , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[27]  Eli Upfal,et al.  Efficient routing in all-optical networks , 1994, STOC '94.

[28]  Frank Thomson Leighton,et al.  Circuit Switching: A Multicommodity Flow Based Approach , 1995 .

[29]  Clifford Stein,et al.  Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs ( Extended Abstract ) , 1998 .

[30]  Eli Upfal,et al.  Constructing disjoint paths on expander graphs , 1987, Comb..

[31]  Aravind Srinivasan,et al.  An extension of the Lovász local lemma, and its applications to integer programming , 1996, SODA '96.

[32]  Alan M. Frieze,et al.  Static and Dynamic Path Selection on Expander Graphs: A Random Walk Approach , 1999, Random Struct. Algorithms.

[33]  Clifford Stein,et al.  Improved approximation algorithms for unsplittable flow problems , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[34]  Prabhakar Raghavan,et al.  Randomized rounding: A technique for provably good algorithms and algorithmic proofs , 1985, Comb..

[35]  Paul Erdös,et al.  On a Combinatorial Game , 1973, J. Comb. Theory, Ser. A.

[36]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[37]  Bruce M. Maggs,et al.  Packet routing and job-shop scheduling inO(congestion+dilation) steps , 1994, Comb..

[38]  Jon M. Kleinberg,et al.  Approximation algorithms for disjoint paths problems , 1996 .

[39]  Bruce M. Maggs,et al.  On-line algorithms for path selection in a nonblocking network , 1990, STOC '90.

[40]  Jeffrey Scott Vitter,et al.  e-approximations with minimum packing constraint violation (extended abstract) , 1992, STOC '92.