By Ronald L. Graham (auth.), Yingfei Dong, Ding-Zhu Du, Oscar Ibarra (eds.)
This booklet constitutes the refereed complaints of the twentieth overseas Symposium on Algorithms and Computation, ISAAC 2009, held in Honolulu, Hawaii, united states in December 2009.
The one hundred twenty revised complete papers provided have been conscientiously reviewed and chosen from 279 submissions for inclusion within the publication. This quantity comprises subject matters equivalent to algorithms and information buildings, approximation algorithms, combinatorial optimization, computational biology, computational complexity, computational geometry, cryptography, experimental set of rules methodologies, graph drawing and graph algorithms, net algorithms, on-line algorithms, parallel and allotted algorithms, quantum computing and randomized algorithms.
Read or Download Algorithms and Computation: 20th International Symposium, ISAAC 2009, Honolulu, Hawaii, USA, December 16-18, 2009. Proceedings PDF
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Extra resources for Algorithms and Computation: 20th International Symposium, ISAAC 2009, Honolulu, Hawaii, USA, December 16-18, 2009. Proceedings
Example text
Definition 6. For a tree G = (V, E), let I(G) denote a set of proper representations in R(G) such that |I(G)| = f ∗ (G) and no two representations in I(G) are stereoisomorphic. Similarly, for each vertex v ∈ V , let I(v) denote a set of proper representations in R(Tv ) such that |I(v)| = f (G, v) and no two representations in I(v) are stereoisomorphic. We call a vertex v ∈ VC with l(v) ∈ {+, −} an asymmetric carbon atom. If l(v) ∈ {cis, trans} then we say that a cis-trans isomer arises around v.
Our first task is to define “stereoisomers” by a mathematically consistent form, which will be given in Section 3. We denote a given chemical graph by G = (V, E) with a vertex set V and an edge set E. The vertex set V is partitioned into VC = {v | v is a carbon atom}, VH = {v | v is a hydrogen atom}, VO = {v | v is an oxygen atom} and VN = {v | v is a nitrogen atom}. We denote |V | = n. Multiple edges are treated as one single edges and the edge set E is partitioned into E1 = {e | e is a single bond}, E2 = {e | e is a double bond} and E3 = {e | e is a triple bond}.
Given a set P of n terminals in the plane, two positive integers k and c with c ≤ (Δ − 1)k, and a topology T0 on the c + 1 subtrees Ti induced by M ST (P ) and k Steiner points, find an optimal placement of k Steiner points to obtain a bottleneck Steiner tree that has the same topology as T0 . The topology T0 in the above problem has c + k + 1 vertices V := {s1 , . . , sk , t1 , . . , tc+1 }, where ti represents subtree Ti and sj represents a Steiner point. See Figure 1. We call each si a Steiner vertex in order to distinguish it from a Steiner point chosen as a point in R2 , and let S := {s1 , .