By Jin Akiyama, Hiro Ito, Toshinori Sakai, Yushi Uno

ISBN-10: 3319485318

ISBN-13: 9783319485317

ISBN-10: 3319485326

ISBN-13: 9783319485324

This booklet constitutes the completely refereed post-conference lawsuits of the 18th eastern convention on Discrete and Computational Geometry and Graphs, JDCDGG 2015, held in Kyoto, Japan, in September 2015.

The overall of 25 papers integrated during this quantity used to be conscientiously reviewed and chosen from sixty four submissions. The papers function advances made within the box of computational geometry and concentrate on rising applied sciences, new technique and purposes, graph thought and dynamics.

This court cases are devoted to Naoki Katoh at the celebration of his retirement from Kyoto University.

**Read Online or Download Discrete and Computational Geometry and Graphs: 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14-16, 2015, Revised Selected Papers PDF**

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**Extra info for Discrete and Computational Geometry and Graphs: 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14-16, 2015, Revised Selected Papers**

**Sample text**

The rest of the paper is organized as follows. Section 2 discusses the case where the centers are constrained to two parallel lines, and presents an O(n log2 n) time algorithm. In Sect. 3 we discuss the unweighted case, where the centers are constrained to two perpendicular lines. We then show that the problem can be solved in O(n log2 n) time. Finally, Sect. 4 concludes the paper with a summary and open problems. 1 Centers Constrained to Two Parallel Lines Preliminaries Let P = {p1 , p2 , . .

While perhaps unsurprising, this result is the ﬁrst analysis of the complexity of dissection. We prove NP-hardness even when the polygons are restricted to be simple (hole-free) and orthogonal. The reduction holds for all cuts that leave the resulting pieces connected, even when rotation and reﬂection are permitted or forbidden. Our proof signiﬁcantly strengthens the observation (originally made by the Demaines during JCDCG’98) that the second half of dissection—re-arranging given pieces into a target shape—is NP-hard: the special case of exact packing rectangles into rectangles can directly simulate 3-Partition [5].

We claim that the collection of TO ’s for all good partition rectangles O is a solution to the Max 5-Partition instance. We will show that this is indeed a valid solution. First, observe again that, because each Ri intersects with at most one partition rectangle, all AO ’s are mutually disjoint. Thus, we now only need to prove that the sum of elements of AO is exactly the target sum p. 46 J. Bosboom et al. Suppose for the sake of contradiction that there exists a good partition rectangle O such that a∈AO a = p.

### Discrete and Computational Geometry and Graphs: 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14-16, 2015, Revised Selected Papers by Jin Akiyama, Hiro Ito, Toshinori Sakai, Yushi Uno

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