TY - JOUR

T1 - Fast algorithms for finding O(congestion + dilation) packet routing schedules

AU - Leighton, Tom

AU - Maggs, Bruce

AU - Richa, Andrea

N1 - Funding Information:
Mathematics Subject Classi cation (1991): 68M20, 68M10, 68M07, 60C05 Tom Leighton is supported in part by ARPA Contracts N00014-91-J-1698 and N00014-92-J-1799. Bruce Maggs is supported in part by an NSF National Young Investigator Award under Grant No. CCR{94{57766, with matching funds provided by NEC Research Institute, and by ARPA Contract F33615{93{1{1330. Part of this research was conducted while Andrea Richa was at Carnegie Mellon University, supported by NSF National Young Investigator Award under Grant No. CCR{94{57766, with matching funds provided by NEC Research Institute, and ARPA Contract F33615{93{1{1330.

PY - 1999

Y1 - 1999

N2 - In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are fixed and edge-simple, there exists a schedule for routing the packets to their destinations in O(c+d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovász Local Lemma and was not constructive. In this paper, we show how to find such a schedule in O(m(c+d)(log℘)4(log log℘)) time, with probability 1-1/℘β, for any positive constant β, where ℘ is the sum of the lengths of the paths taken by the packets in the network, and m is the number of edges used by some packet in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lovász Local Lemma discovered by Beck.

AB - In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are fixed and edge-simple, there exists a schedule for routing the packets to their destinations in O(c+d) steps using constant-size queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovász Local Lemma and was not constructive. In this paper, we show how to find such a schedule in O(m(c+d)(log℘)4(log log℘)) time, with probability 1-1/℘β, for any positive constant β, where ℘ is the sum of the lengths of the paths taken by the packets in the network, and m is the number of edges used by some packet in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct the schedules is based on the algorithmic form of the Lovász Local Lemma discovered by Beck.

UR - http://www.scopus.com/inward/record.url?scp=0000897531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000897531&partnerID=8YFLogxK

U2 - 10.1007/s004930050061

DO - 10.1007/s004930050061

M3 - Article

AN - SCOPUS:0000897531

VL - 19

SP - 375

EP - 401

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 3

ER -