Polynomial-Time Construction of Linear Network Coding

  • Authors:

  • Kazuo Iwama;Harumichi Nishimura;Mike Paterson;Rudy Raymond;Shigeru Yamashita

  • Affiliations:

  • School of Informatics, Kyoto University, Japan;School of Science, Osaka Prefecture University, Japan;Department of Computer Science and DIMAP, University of Warwick, UK;Tokyo Research Laboratory, IBM Japan, Japan;Graduate School of Information Science, Nara Inst. of Science & Technology, Japan

  • Venue:
  • ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
  • Year:
  • 2008

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Abstract

Constructing k independent sessions between k source-sink pairs with the help of a linear operation at each vertex is one of the most standard problems in network coding. For an unbounded k, this is known to be NP-hard. Very recently, a polynomial-time algorithm was given for k = 2 [Wang and Shroff, ISIT 2007], but was open for a general (constant) k. This paper gives a polynomial-time algorithm for this problem under the assumption that the size of the finite field for the linear operations is bounded by a fixed constant.