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Fast On-Line/Off-Line Algorithms for Optimal Reinforcement of a Network and Its Connections with Principal Partition

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FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1974))

Abstract

The problem of computing the strength and performing optimal reinforcement for an edge-weighted graph G(V, E,w) is well-studied [1],[2],[3],[6],[7],[9]. In this paper, we present fast (sequential linear time and parallel logarithmic time) on-line algorithms for optimally reinforcing the graph when the reinforcement material is available continuosly online. These are first on-line algortithms for this problem. Although we invest some time in preprocessing the graph before the start of our algorithms, it is also shown that the output of our on-line algorithms is as good as that of the off-line algorithms, making our algorithms viable alternatives to the fastest off-line algorithms in situtations when a sequence of more than O(|V|) reinforcement problems need to be solved. In such a situation the time taken for preprocessing the graph is less that the time taken for all the invocations of the fastest off-line algorithms. Thus our algorithms are also efficient in the general sense. The key idea is to make use of the theory of Principal Partition of a Graph. Our results can be easily generalized to the general setting of principal partition of nondecreasing submodular functions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology - Bombay, 400 076, Mumbai, India

    Sachin B. Patkar

  2. Department of Electrical Engg., Indian Institute of Technology - Bombay, 400 076, Mumbai, India

    H. Narayanan

Authors
  1. Sachin B. Patkar
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  2. H. Narayanan
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Delhi, Hauz Khas, 110016, New Delhi, India

    Sanjiv Kapoor  & Sanjiva Prasad  & 

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Patkar, S.B., Narayanan, H. (2000). Fast On-Line/Off-Line Algorithms for Optimal Reinforcement of a Network and Its Connections with Principal Partition. In: Kapoor, S., Prasad, S. (eds) FST TCS 2000: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2000. Lecture Notes in Computer Science, vol 1974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44450-5_7

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  • DOI: https://doi.org/10.1007/3-540-44450-5_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41413-1

  • Online ISBN: 978-3-540-44450-3

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