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Vertex-Weighted Matching in Two-Directional Orthogonal Ray Graphs

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

Let G denote an n-vertex two-directional orthogonal ray graph. A bicolored 2D representation of G requires only O(n) space, regardless of the number of edges in G. Given such a compact representation of G, and a (possibly negative) weight for each vertex, we show how to compute a maximum weight matching of G in O(nlog2 n) time. The classic problem of scheduling weighted unit tasks with release times and deadlines is a special case of this problem, and we obtain an O(nlogn) time bound for this special case. As an application of our more general result, we obtain an O(nlog2 n)-time algorithm for computing the VCG outcome of a sealed-bid unit-demand auction in which each item has two associated numerical parameters (e.g., third-party “quality” and “seller reliability” scores) and each bid specifies the amount an agent is willing to pay for any item meeting specified lower bound constraints with respect to these two parameters.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, USA

    C. Gregory Plaxton

Authors
  1. C. Gregory Plaxton
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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Plaxton, C.G. (2013). Vertex-Weighted Matching in Two-Directional Orthogonal Ray Graphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_49

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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