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Tree-Breadth of Graphs with Variants and Applications

Leitert, Arne
http://rave.ohiolink.edu/etdc/view?acc_num=kent1497402176814598

Abstract Details

2017, PHD, Kent State University, College of Arts and Sciences / Department of Computer Science.
The tree-breadth of a graph is a recently introduced variant of the well known idea of decomposing a graph into a tree of bags. It is a parameter which adds a metric constraint to tree-decompositions limiting the radius of each bag. In this dissertation, we further investigate the tree-breadth of graphs. We present approaches to compute a tree-decomposition with small breadth for a given graph including approximation algorithms for general graphs as well as optimal solutions for special graph classes. Additionally, we introduce a variant of tree-breadth called strong tree-breadth. Next, we present various algorithms to approach the (Connected) r-Domination problem for graphs with bounded tree-breadth. One variant, called path-breadth, requires the decomposition to be a path instead of a tree. We use graphs with bounded path-breadth to construct efficient constant-factor approximation algorithms for the bandwidth and line-distortion problems. Motivated by these results, we introduce and investigate the new Minimum Eccentricity Shortest Path problem. We analyse the hardness of the problem, show algorithms to compute an optimal solution, and present approximation algorithms differing in quality and runtime.
Feodor Dragan (Advisor)
Computer Science

Recommended Citations

Citations

  • Leitert, A. (2017). Tree-Breadth of Graphs with Variants and Applications [Doctoral dissertation, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497402176814598

    APA Style (7th edition)

  • Leitert, Arne. Tree-Breadth of Graphs with Variants and Applications. 2017. Kent State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1497402176814598.

    MLA Style (8th edition)

  • Leitert, Arne. "Tree-Breadth of Graphs with Variants and Applications." Doctoral dissertation, Kent State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=kent1497402176814598

    Chicago Manual of Style (17th edition)

kent1497402176814598
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© 2017, all rights reserved.
This open access ETD is published by Kent State University and OhioLINK.