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Positive Semidefinite Zero Forcing: Complexity and Lower Bounds

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Algorithms and Data Structures (WADS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9214))

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Abstract

The positive semidefinite zero forcing number of a graph is a parameter that is important in the study of minimum rank problems. In this paper, we focus on the algorithmic aspects of computing this parameter. We prove that it is NP-complete to find the positive semidefinite zero forcing number of a given graph, and this problem remains NP-complete even for graphs with maximum vertex degree 7. We present a linear time algorithm for computing the positive semidefinite zero forcing number of generalized series-parallel graphs. We introduce the constrained tree cover number and apply it to improve lower bounds for positive semidefinite zero forcing. We also give formulas for the constrained tree cover number and the tree cover number on graphs with special structures.

Research supported in part by an NSERC Discovery Research Grant, Application No.: RGPIN-2013-261290.

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Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, Canada

    Boting Yang

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  1. Boting Yang
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Correspondence to Boting Yang .

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Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. Carleton University, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. University of Victoria, Victoria, Canada

    Ulrike Stege

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Yang, B. (2015). Positive Semidefinite Zero Forcing: Complexity and Lower Bounds. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_52

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  • DOI: https://doi.org/10.1007/978-3-319-21840-3_52

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21839-7

  • Online ISBN: 978-3-319-21840-3

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