Direct routing: Algorithms and complexity

Costas Busch, Malik Magdon-Ismail, Marios Mavronicolas, Paul Spirakis

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Direct routing is the special case of bufferless routing where N packets, once injected into the network, must be delivered to their destinations without collisions. We give a general treatment of three facets of direct routing: 1. Algorithms. We present a polynomial-time greedy direct algorithm which is worst-case optimal. We improve the hound of the greedy algorithm for special cases, by applying variants of this algorithm to commonly used network topologies. In particular, we obtain near-optimal routing time for the tree. mesh, butterfly, and hypercube. 2. Complexity. By a reduction from Vertex Coloring, we show that optimal Direct Routing is inapproximable, unless P = NP. 3. Lower Bounds for Buffering. We show that certain direct routing problems cannot be solved efficiently; in order to solve these problems, any routing algorithm needs buffers. We give non-trivial lower bounds on such buffering requirements for general routing algorithms.

Original languageEnglish (US)
Pages (from-to)45-68
Number of pages24
JournalAlgorithmica (New York)
Issue number1
StatePublished - Jun 2006
Externally publishedYes


  • Bufferless routing
  • Communication algorithms
  • Congestion
  • Dilation
  • Direct routing

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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