Computing the throughput of Concatenation State Machines

  • Authors:

  • Jurek Czyzowicz;Wojciech Fraczak;Mohammadreza Yazdani

  • Affiliations:

  • Département d'informatique, Université du Québec en Outaouais, Gatineau, PQ, Canada;Département d'informatique, Université du Québec en Outaouais, Gatineau, PQ, Canada and IDT Canada, Ottawa, ON, Canada;IDT Canada, Ottawa, ON, Canada and Department of Systems and Computer Engineering, Carleton University, Ottawa, ON, Canada

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2008

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Abstract

Concatenation State Machine (CSM) is a labeled directed And-Or graph representing a deterministic push-down transducer. In the high-performance version of CSM, labels associated to edges are words (rather than letters) over the input alphabet. The throughput of a path p is defined as the sum of the lengths of the labels of the path, divided by the number of edges of p. The throughput of a CSM M is defined as the infimum of the throughput of all accepting paths of M. In this paper we give an O(nmlog(max-min@e)) algorithm, computing an @e-approximation of the throughput of a CSM M, where n is the number of nodes, m is the number of edges, and max (min) is the maximum (respectively, minimum) of the lengths of the edge labels of M. While we have been interested in a particular case of an And-Or graph representing a transducer, we have actually solved the following problem: if a real weight function is defined on the edges of an And-Or graph G, we compute an @e-approximation of the infimum of the complete hyper-path mean weights of G. This problem, if restricted to digraphs, is strongly connected to the problem of finding the minimum cycle mean.