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Single Source Shortest Paths for All Flows with Integer Costs

Author Tadao Takaoka

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Tadao Takaoka

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Tadao Takaoka. Single Source Shortest Paths for All Flows with Integer Costs. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 56-67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/OASIcs.ATMOS.2015.56

Abstract

We consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity. The problem is to push an unsplittable flow $f$ from a specified source to all other vertices with the minimum cost for all f values. Let G = (V, E) with |V| = n and |E| = m. If there are t different capacity values, we can solve the single source shortest path problem t times for all f in O(tm + tn log n) time, which is O(m^2) when t = m. We improve this time to O(min{t, cn}m + cn^2), which is less than O(cmn) if edge costs are non-negative integers bounded by c. Our algorithm performs better for denser graphs.
Keywords
  • information sharing
  • shortest path problem for all flows
  • priority queue
  • limited edge cost
  • transportation network

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