Discrete and Computational Geometry: Japanese Conference, by Bernardo M. Ábrego, Esther M. Arkin (auth.), Jin Akiyama,

By Bernardo M. Ábrego, Esther M. Arkin (auth.), Jin Akiyama, Mikio Kano, Xuehou Tan (eds.)

This ebook constitutes the completely refereed post-proceedings of the japanese convention on Discrete Computational Geometry, JCDCG 2004, held in Tokyo, Japan in October 2004, to honor János Pach on his 50th year.

The 20 revised complete papers provided have been rigorously chosen in the course of rounds of reviewing and development from over 60 talks on the convention. All present matters in discrete algorithmic geometry are addressed.

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Additional info for Discrete and Computational Geometry: Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004, Revised Selected Papers

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These points will uniquely determine all other elements of C, according to the following rules. Let b2 be the point at distance 2 from both c1 and a2 , which lies to the right of the line c1 a2 . Once b2 is defined, let c2 be the point on the x-axis, different from c1 , whose distance from b2 is 2. In general, if bi and ci have already been defined, let bi+1 denote the point at distance 2 from both ci and ai+1 , lying on the right-hand side of their connecting line, and let ci+1 = ci be the (other) point of the x-axis at distance 2 from bi+1 .

Any critical set in G contains at most Nd vertices where Nd = d(d + 1) . d−2 Proof. Let X be a critical set in G. For every vertex v ∈ X, its degree in G[X] is bounded by d + 2, dX (v) ≤ d + 2. Therefore dX (v) ≤ (d + 2)|X|. 2i(X) = v∈X On the other hand, i(X) = S(|X|, d) since X is critical. We assume that |X| > and d + 1 (the lemma follows otherwise). Therefore S(|X|, d) = |X|d − d+1 2 2i(X) = 2d|X| − d(d + 1) ≤ (d + 2)|X|, (d − 2)|X| ≤ d(d + 1), d(d + 1) , |X| ≤ d−2 |X| ≤ Nd . Algorithm 2. // Given a M -independent graph G with ∆(G) ≤ d + 2 and δ(G) ≤ d + 1, // find a sequence of vertex additions and edge splits that creates G.

344–356, 2002. Springer-Verlag. 5. F. Lam, M. Alexandersson, and L. Pachter. Picking alignments from (Steiner) trees. Journal of Computational Biology, 10:509–520, 2003. edu Abstract. Let Rd (G) be the d-dimensional rigidity matroid for a graph G = (V, E). Combinatorial characterization of generically rigid graphs is known only for the plane d = 2 [11]. e. has maximum degree at most d + 2 and minimum degree at most d + 1. We present three efficient algorithms for sparse graphs G that (i) detect if E is independent in the rigidity matroid for G, and (ii) construct G using vertex insertions preserving if G is isostatic, and (iii) compute the rank of Rd (G).

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