ESA 2004: Algorithms – ESA 2004 pp 134-145

# Direct Routing: Algorithms and Complexity

• Costas Busch
• Malik Magdon-Ismail
• Marios Mavronicolas
• Paul Spirakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3221)

## Abstract

Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be routed along specific paths to their destinations without conflicts. We give a general treatment of three facets of direct routing:

• Algorithms. We present a polynomial time greedy algorithm for arbitrary direct routing problems which is worst-case optimal, i.e., there exist instances for which no direct routing algorithm is better than the greedy. We apply variants of this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time for the tree and d-dimensional mesh, given arbitrary sources and destinations; for the butterfly and the hypercube, the same result holds for random destinations.

• Complexity. By a reduction from Vertex Coloring, we show that Direct Routing is inapproximable, unless P=NP.

• Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.

## Keywords

Greedy Algorithm Injection Time Chromatic Number Dependency Graph Direct Route
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Costas Busch
• 1
• Malik Magdon-Ismail
• 1
• Marios Mavronicolas
• 2
• Paul Spirakis
• 3
1. 1.Department of Computer ScienceRensselaer Polytechnic InstituteTroyUSA
2. 2.Department of Computer ScienceUniversity of CyprusNicosiaCyprus
3. 3.Department of Computer Engineering and InformaticsUniversity of Patras, RionPatrasGreece