Optimal shooting: Characterizations and applications

Bauernöppel, Frank; Kranakis, Evangelos; Kriz̧anc, Danny; Maheshwari, Anil; Noy, Marc; Sack, Jörg-Rüdiger; Urrutia, Jorge

doi:10.1007/3-540-60084-1_76

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“…The results for interval graphs were extended to circular arc graphs (intersection graphs of arcs of a circle) [18]. In an entirely different approach, Matching can also be solved very efficiently in permutation graphs (intersection graphs of line segments connecting two parallel lines) [30]; see also [9] for an (unpublished) matchingalgorithm for permutation graphs that is slower but beautifully uses range queries to find the matching. We should note that RDV graphs are unrelated to circular arc graphs and permutation graphs (i.e., neither a subclass nor a superclass); Figure 1 gives a specific example.…”

Section: Other Related Resultsmentioning

confidence: 99%

Finding Large Matchings in 1-Planar Graphs of Minimum Degree 3

Biedl

Klute

2020

Graph-Theoretic Concepts in Computer Science

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In this paper, we study the maximum matching problem in RDV graphs, i.e., graphs that are vertex-intersection graphs of downward paths in a rooted tree. We show that this problem can be reduced to a problem of testing (repeatedly) whether a vertical segment intersects one of a dynamically changing set of horizontal segments, which in turn reduces to an orthogonal ray shooting query. Using a suitable data structure, we can therefore find a maximum matching in O(n log n) time (presuming a linear-sized representation of the graph is given), i.e., without even looking at all edges.

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Section: Other Related Resultsmentioning

confidence: 99%