Universal O(congestion + dilation + log1+εN) local control packet switching algorithms

In 1988, Leighton, Maggs and Rao proved a much celebrated result: that for any network, given any collection of packets with a specified route for each packet, there exists an “optimal” schedule for all these packets. That is, there exists a schedule of the motion of the packets such that at each step, every edge is crossed by at most one packet, and all the packets are delivered to their destinations in O(C + D) steps, where C is the “congestion” (i.e., the maximum number of paths that share the same edge), and D is the “dilation” (i.e., the length of the longest path). The proof was non-constructive and relied on Lovász Local Lemma. In a followup paper, Leighton, Maggs, and Richa gave a centralized algorithm for finding the schedule. The original paper left open the question whether there exists a constructive distributed “on-line” algorithm with the same optimal performance. Last year, Rabani and Tardos presented a randomized local-control algorithm which with high probability delivers all packets in time O ( C + D · ( (log∗ N) ∗ N) ) + + (log N) ) . In this paper, we show a nearly optimal local control algorithm for this long-standing open problem. That is, we show a randomized local control algorithm which for any network topology delivers all the packets to their destinations in time O(C + D +log N) with high probability, where N is the size of the problem, and > 0 is arbitrary. Our result has implications to ATM (Asynchronous Transfer Mode) packet switching algorithms and other applications. ∗Bell Communications Research, MCC-1C365B, Morristown, NJ 07960-6438, USA. Email: rafail@bellcore.com †Computer Science Department, Technion — IIT, Haifa 32000, Israel. Part of this work was done while visiting Bell Communications Research. Work supported by grants from the Fund for the Promotion of Sponsored Research and from the Fund for the Promotion of Research at the Technion, and by a David and Ruth Moskowitz Academic Lecturship award. Email: rabani@cs.technion.ac.il

[1]  Friedhelm Meyer auf der Heide,et al.  Universal algorithms for store-and-forward and wormhole routing , 1996, STOC '96.

[2]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks: the multiple node case , 1994, TNET.

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

[4]  Inder S. Gopal.  Multimedia networking: applications and challenges , 1994, PODC '94.

[5]  Bruce M. Maggs,et al.  Randomized Routing and Sorting on Fixed-Connection Networks , 1994, J. Algorithms.

[6]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the single node case , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[7]  Friedhelm Meyer auf der Heide,et al.  A Packet Routing Protocol for Arbitrary Networks , 1995, STACS.

[8]  József Beck,et al.  An Algorithmic Approach to the Lovász Local Lemma. I , 1991, Random Struct. Algorithms.

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

[10]  Baruch Awerbuch,et al.  Universal stability results for greedy contention-resolution protocols , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[11]  Lisa Zhang,et al.  General dynamic routing with per-packet delay guarantees of O(distance+1/session rate) , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[12]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the multiple node case , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[13]  Yuval Rabani,et al.  Distributed packet switching in arbitrary networks , 1996, STOC '96.

[14]  Nsf Ncr,et al.  A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single Node Case* , 1991 .

[15]  Alan M. Frieze,et al.  A general approach to dynamic packet routing with bounded buffers , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[16]  Aravind Srinivasan,et al.  A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria , 1997, STOC '97.

[17]  Serge A. Plotkin.  Competitive Routing of Virtual Circuits in ATM Networks , 1995, IEEE J. Sel. Areas Commun..

[18]  Frank Thomson Leighton,et al.  Methods for message routing in parallel machines , 1992, STOC '92.

[19]  Allan Borodin,et al.  Adversarial queueing theory , 1996, STOC '96.