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Approximate TSP in Graphs with Forbidden Minors [chapter]

Michelangelo Grigni
2000 Lecture Notes in Computer Science  
These results imply (i) a QPTAS (quasi-polynomial time approximation scheme) for the TSP (traveling salesperson problem) in unweighted graphs with an excluded minor, and (ii) a QPTAS for the TSP in weighted  ...  The second algorithm nds a spanner with small stretch factor, and is analyzed for graphs in a hereditary family G(k).  ...  Acknowledgment: We thank Robin Thomas for help with Lemma 10. References  ... 
doi:10.1007/3-540-45022-x_73 fatcat:s3un4gipwfevhfyho2rfho4iiy

Finding Light Spanners in Bounded Pathwidth Graphs [article]

Michelangelo Grigni, Hao-Hsiang Hung
2012 arXiv   pre-print
For weighted graphs from several minor-closed graph families, the existence of light spanners has been essential in the design of approximation schemes for the metric TSP (the traveling salesman problem  ...  In this paper we make some progress towards the conjecture that light spanners exist for every minor-closed graph family. In particular, we show that they exist for graphs with bounded pathwidth.  ...  [5, Thm. 2] implies a PTAS for metric TSP when G is any graph class with a fixed forbidden minor.  ... 
arXiv:1104.4669v2 fatcat:ovxe3r27ojg5jl7w3mvzjo3oii

Light Spanners in Bounded Pathwidth Graphs [chapter]

Michelangelo Grigni, Hao-Hsiang Hung
2012 Lecture Notes in Computer Science  
In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem).  ...  We have developed an efficient algorithm for light spanners in bounded pathwidth graphs, based on an intermediate data structure called monotone tree.  ...  We have discussed the major difficulty in handling bounded treewidth graphs in [9] : we have no control over the MST topology inside of the bounded treewidth graphs, and a trimming might introduce too  ... 
doi:10.1007/978-3-642-32589-2_42 fatcat:md5obquxgvfdjjmxps7ht4srti

Theoretical and Computational Methods for Network Design and Routing

Ziye Tang
2021
For instance, approximation algorithms, developed by theoretical computer scientists, are able to produce solutions with a provable worst-case guarantee but can be too pessimistic for practical applications  ...  Traditionally, however, techniques from these fields are developed separately with their own strengths and weaknesses.  ...  Acknowledgments First and foremost, I would like to thank my advisor Willem-Jan van Hoeve. Under your continuous guid-  ... 
doi:10.1184/r1/16915192 fatcat:ourpzwpg7ng6zbufsbjtk6m3aq

Computational Geometry (Dagstuhl Seminar 13101) Scheduling (Dagstuhl Seminar 13111) Future Internet (Dagstuhl Seminar 13131)

Otfried Cheong, Kurt Mehlhorn, Monique, Susanne Albers, Onno Boxma, Kirk, Erik Demaine, Fedor Fomin, Mohammadtaghi Hajiaghayi, Dimitrios, Jon Crowcroft, Markus Fidler (+2 others)
2013 unpublished
In Graph minors III, Robertson and Seymour write: "It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal?  ...  structures are originated in Graph Minors of Robertson and Seymour, because of the structure of the graphs excluding some fixed some graph as a minor.  ...  What we want is some way to feed in some constraints and out comes a prescription for a network architecture -we can then fire up the traditional tools (graph theory, queueing theory, control theory, etc  ... 
fatcat:6benpx4q2rfbzjefimwstubfoe

The problem of many: efficient multi-arm, multi-object task and motion planning with optimality guarantees

Rahul Shome
2020
A key focus corresponds to overcoming scalability challenges in motion planning and dealing with hybrid planning domains, i.e., those that combine continuous and discrete action spaces, to solve manipulation  ...  The work addresses the theoretical gap that existed in modeling interactions with the boundaries of the collision-free space, which invariably arise in task planning for manipulation.The second contribution  ...  These methods are based on underlying graph spanners (Algo 4), which refer to subgraphs that trade-off connectivity and path-costs.  ... 
doi:10.7282/t3-8fcf-xp94 fatcat:m2eb2koobndzfoixxqkrukmziy