Binhai Zhu

Combinatorial Optimization and Applications

The Seventh Annual International Conference on Combinatorial Optimization and Applications, abbreviated as COCOA 2013, was held during December 12–14, 2013 in Chengdu, China. Some of the best papers for COCOA’2013 were invited to be published in this special issue of Theoretical Computer Science. The nine selected papers are across computational geometry, computational biology, on-line algorithms, graph theory, parameterized complexity and social networks. The first paper is “An Inductive Construction of Minimally Rigid Body–Hinge Simple Graphs”, by Yuki Kobayashi et al. The authors showed that a minimally rigid body–hinge simple graph can be constructed with five elementary operations in polynomial time. The second paper “Mining Hidden Links in Social Networks to Achieve Equilibrium”, by Huan Ma et al., focuses on mining interesting links in a complex social network. While the problem is NP-hard, interesting empirical results are obtained. In the third paper “A Loopless Algorithm for Generating Multiple Binary Tree Sequences Simultaneously”, Ro-Yu Wu et al. studied the problem of generating binary trees using two extra LCand RC-sequences. A loopless algorithm is presented. In the fourth paper “Following a Curve with the Discrete Frechet Distance”, Tim Wylie and Binhai Zhu studied the problem of fitting a polygonal curve with a set of given points under the discrete Frechet distance. Several different versions of the problems are studied, some are in P and some are NP-complete. In the fifth paper “Touring a Sequence of Disjoint Polygons: Complexity and Extension”, Arash Ahadi, Amirhossein Mozafari and Alireza Zarei proved that the problem of touring a set of disjoint polygons with a shortest path between a given source and a given sink is NP-hard, solving a long-standing open problem. The previous NP-hardness result only holds when the polygons could be overlapping. In the sixth paper “Circular Convex Bipartite Graphs: Feedback Vertex Sets”, Tian Liu et al. showed that the famous NP-complete feedback vertex set problem is polynomially solvable on a circular convex bipartite graph. The solution is obtained by using Turing reductions. In the seventh paper “Approximating the Maximum Multiple RNA Interaction Problem”, Weitian Tong et al. presented new approximation algorithms for two variations of the maximum multiple RNA interaction problem. In the eighth paper “Online Bin Covering: Expectations vs. Guarantees”, Marie Christ, Lene Favrholdt and Kim Larsen analyzed the performance of two classic online algorithms HARMONIC and NEXT-FIT for the bin covering problem. Several different performance measures are used. In the ninth paper “Parameterized and Approximation Algorithms for Finding two Disjoint Matchings”, Zhi-Zhong Chen, Ying Fan and Lusheng Wang studied the problem of computing two disjoint matching in weighted and unweighted graphs. They gave an FPT algorithm for the problem on unweighted graph and an approximation algorithm for the problem on a weighted graph. We thank Sichuan University for hosting the conference, all the authors for submitting their contributions and the timely work of all the reviewers. Finally, we thank Giorgio Ausiello for his assistance and the program committee of COCOA 2013 (who helped select and review the papers).

Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations

This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point by simply “walking through” the triangulation, after selecting a “good starting point” by random sampling. The analysis generalizes and extends a recent result for dD 2 dimensions by proving this procedure takes expected time close to O.n 1=.dC1/ / for point location in Delaunay triangulations of n random points indD 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice.

A Note on Point Location in Delaunay Triangulations of Random Points

Abstract. This short note considers the problem of point location in a Delaunay triangulation of n random points, using no additional preprocessing or storage other than a standard data structure representing the triangulation. A simple and easy-to-implement (but, of course, worst-case suboptimal) heuristic is shown to take expected time O(n1/3) .

Guarding polyhedral terrains

Abstract We prove that ⌊ n 2 ⌋ vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that ⌊ (4n − 4) 13 ⌋ edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ⌊ n 3 ⌋ (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color theorem, no practical polynomial time algorithm achieving these bounds seems to exist, but we present a linear time algorithm for placing ⌊ 3n 5 ⌋ vertex guards for covering a polyhedral terrain and a linear time algorithm for placing ⌊ 2n 5 ⌋ edge guards.

On recovering syntenic blocks from comparative maps

A genomic map is represented by a sequence of gene markers, and a gene marker can appear in several different genomic maps, in either positive or negative form. A strip (syntenic block) is a sequence of distinct markers that appears as subsequences in two or more maps, either directly or in reversed and negated form. Given two genomic maps G and H, the problem Maximal Strip Recovery (MSR) is to find two subsequences G′ and H′ of G and H, respectively, such that the total length of disjoint strips in G′ and H′ is maximized. Previously only a heuristic was provided for this problem, which does not guarantee finding the optimal solution, and it was unknown whether the problem is NP-hard or polynomially solvable. In this paper, we develop a factor-4 polynomial-time approximation algorithm for the problem, and show that several close variants of the problem are intractable.

The approximability of the exemplar breakpoint distance problem

In this paper we present the first set of approximation and inapproximability results for the Exemplar Breakpoint Distance Problem. Our inapproximability results hold for the simplest case between only two genomes \({\cal G}\) and \({\cal H}\), each containing only one sequence of genes (possibly with repetitions).

WebSail: from on-line learning to Web search

In this paper we report our research on building WebSail, an intelligent web search engine that is able to perform real-time adaptive learning. WebSail learns from the users relevance feedback, so that it is able to speed up its search process and to enhance its search performance. We design an efficient adaptive learning algorithm TW2 to search for web documents. WebSail employs TW2 together with an internal index database and a real-time meta-searcher to perform real-time adaptive learning to find desired documents with as little relevance feedback from the user as possible. The architecture and performance of WebSail are also discussed.

Linear Time Probabilistic Algorithms for the Singular Haplotype Reconstruction Problem from SNP Fragments

In this paper, we develop a probabilistic model to approach two realistic scenarios regarding the singular haplotype reconstruction problem--the incompleteness and inconsistency that occurred in the DNA sequencing process to generate the input haplotype fragments, and the common practice used to generate synthetic data in experimental algorithm studies. We design three algorithms in the model that can reconstruct the two unknown haplotypes from the given matrix of haplotype fragments with provable high probability and in linear time in the size of the input matrix. We also present experimental results that conform with the theoretical efficient performance of those algorithms. The software of our algorithms is available for public access and for real-time on-line demonstration.

Efficient Algorithms for the Closest String and Distinguishing String Selection Problems

In the paper, we study three related problems, the closest string problem, the farthest string problem and the distinguishing string selection problem. These problems have applications in motif detection, binding sites locating, genetic drug target identification, genetic probes design, universal PCR primer design, etc. They have been extensively studied in recent years. The problems are defined as follows: The closest string problem: given a group of strings

The canadian traveller problem and its competitive analysis

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