6.889: Algorithms for Planar Graphs and Beyond (Fall 2011)

Erik Demaine, Shay Mozes, Christian Sommer, Siamak Tazari

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[+] Contraction decomposition of bounded-genus and H-minor-free graphs: PTASs, FPT algortihms, k-cut, radial coloring, tight roots, radially shortest paths, te structures

This lecture is about contraction decomposition: partitioning the edges of the graph into k pieces (for a specified integer k ≥ 2) such that contracting any piece reduces the graph down to bounded treewidth. We've already seen in Lecture 15 how to do this for planar graphs. In this lecture, we see how to do it in bounded-genus graphs in detail, and H-minor-free graphs at a high level. We also briefly discuss applications of contraction decomposition to PTASs and FPT algorithms. The H-minor-free contraction decomposition is a new result from STOC 2011 by Demaine, Hajiaghayi, and Kawarabayashi.

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Lecture notes, page 1/7[previous page][next page][PDF]

Lecture notes, page 1/7[previous page][next page][PDF]

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