Jianer Chen

Vertex Cover

Recently, there has been increasing interest and progress in lowering the worst-case time complexity for well-known NP-hard problems, particularly for the Vertex Cover problem. In this paper, new properties for the Vertex Cover problem are indicated, and several simple and new techniques are introduced, which lead to an improved algorithm of time O(kn+1.2852k) for the problem. Our algorithm also induces improvement on previous algorithms for the Independent Set problem on graphs of small degree.

Parameterized and Exact Computation

We consider the problem of extracting a maximum-size reflect ed network in a linear program. This problem has been studied before and a st ate-of-the-art SGA heuristic with two variations have been proposed. In this paper we apply a new approach to evaluate the quality o f SGA. In particular, we solve majority of the instances in the testbe d to optimality using a new fixed-parameter algorithm, i.e., an algorithm whose run time is polynomial in the input size but exponential in terms of an additional para meter associated with the given problem. This analysis allows us to conclude that the the existing SGA heuristic, in fact, produces solutions of a very high quality and often reaches t optimal objective values. However, SGA contain two components which leave som e space for improvement: building of a spanning tree and searching for an i ndependent set in a graph. In the hope of obtaining even better heuristic, we tri ed to replace both of these components with some equivalent algorithms. We tried to use a fixed-parameter algorithm instead of a greed y one for searching of an independent set. But even the exact solution of this subproblem improved the whole heuristic insignificantly. Hence, the crucial par t of SGA is building of a spanning tree. We tried three different algorithms, and it a ppears that the DepthFirst search is clearly superior to the other ones in buildin g of the spanning tree for SGA. Thereby, by application of fixed-parameter algorithms, we m anaged to check that the existing SGA heuristic is of a high quality and selec ted the component which required an improvement. This allowed us to intensify the research in a proper direction which yielded a superior variation of SGA. This variation significantly improves the results of the basic SGA solving most of the instances in our experiments to optimality in a short time. A preliminary version of this paper will appear in the Procee dings of the 4th International Workshop on Parameterized and Exact Computation (IWPEC’09). Department of Computer Science, Royal Holloway, Universit y of London, Egham, Surrey TW20 0EX, England, UK,gutin@cs.rhul.ac.uk Department of Computer Science, Royal Holloway, Universit y of London, Egham, Surrey TW20 0EX, England, UK,daniel.karapetyan@gmail.com Department of Computer Science, University College Cork, I reland,i.razgon@cs.ucc.ieThe Workshop on Parameterized and Exact Computation (IWPEC) is an - ternational workshop series that covers research in all aspects of parameterized and exact algorithms and complexity, and especially encourages the study of parameterized and exact computations for real-world applications and algori- mic engineering. The goal of the workshop is to present recent research results, including signi?cant work-in-progress,and to identify and explore directions for future research. IWPEC2009wasthefourthworkshopintheseries,heldinCopenhagen,D- mark, during September 10-11, 2009. The workshop was part of ALGO 2009, which also hosted the 17th European Symposium on Algorithms (ESA 2009), the 9th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2009), and the 7th Workshop on Appr- imation and Online Algorithms (WAOA 2009). Three previous meetings of the IWPEC series were held in Bergen, Norway, 2004, Zu rich, Switzerland, 2006, and Victoria, Canada, 2008. At IWPEC 2009, we had two plenary speakers,Noga Alon (Tel Aviv Univ- sity, Israel) and Hans Bodlaender (Utrecht University, The Netherlands), giving 50-minutetalkseach.ProfessorAlonspokeon ColorCoding,BalancedHashing andApproximateCounting, andProfessorBodlaenderon Kernelization:New Upper and Lower Bound Techniques. Their respective abstracts accompanying the talks are included in these proceedings. InresponsetotheCallforPapers,52papersweresubmitted.Eachsubmission was reviewed by at least three reviewers (most by at least four). The reviewers were either Program Committee members or invited external reviewers. The ProgramCommittee held electronic meetings using the EasyChair system, went throughthoroughdiscussions,andselected25ofthesubmissionsforpresentation at the workshop and inclusion in this LNCS volume

Improved upper bounds for vertex cover

This paper presents an O(1.2738^k+kn)-time polynomial-space algorithm for Vertex Cover improving the previous O(1.286^k+kn)-time polynomial-space upper bound by Chen, Kanj, and Jia. Most of the previous algorithms rely on exhaustive case-by-case branching rules, and an underlying conservative worst-case-scenario assumption. The contribution of the paper lies in the simplicity, uniformity, and obliviousness of the algorithm presented. Several new techniques, as well as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis. The algorithm also improves the O(1.2745^kk^4+kn)-time exponential-space upper bound for the problem by Chandran and Grandoni.

Tight lower bounds for certain parameterized NP-hard problems

Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time n/sup o(k)/poly(m), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t - l)-st level W[t

A Fast Hierarchical Clustering Algorithm for Functional Modules Discovery in Protein Interaction Networks

1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted SAT, dominating set, hitting set, set cover, and feature set, cannot be solved in time n/sup o(k)/poly(m), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[l] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weighted q-SAT (for any fixed q /spl ges/ 2), clique, and independent set, cannot be solved in time n/sup o(k)/ unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n/sup k/ poly(m) or O(n/sup k/).

Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size

As advances in the technologies of predicting protein interactions, huge data sets portrayed as networks have been available. Identification of functional modules from such networks is crucial for understanding principles of cellular organization and functions. However, protein interaction data produced by high-throughput experiments are generally associated with high false positives, which makes it difficult to identify functional modules accurately. In this paper, we propose a fast hierarchical clustering algorithm HC-PIN based on the local metric of edge clustering value which can be used both in the unweighted network and in the weighted network. The proposed algorithm HC-PIN is applied to the yeast protein interaction network, and the identified modules are validated by all the three types of Gene Ontology (GO) Terms: Biological Process, Molecular Function, and Cellular Component. The experimental results show that HC-PIN is not only robust to false positives, but also can discover the functional modules with low density. The identified modules are statistically significant in terms of three types of GO annotations. Moreover, HC-PIN can uncover the hierarchical organization of functional modules with the variation of its parameters value, which is approximatively corresponding to the hierarchical structure of GO annotations. Compared to other previous competing algorithms, our algorithm HC-PIN is faster and more accurate.

Strong computational lower bounds via parameterized complexity

Determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data reduction algorithm to reduce an instance of a parameterized problem to an equivalent smaller instance (i.e., a kernel) has led to very efficient algorithms and now goes hand-in-hand with the design of practical algorithms for solving

Improved algorithms for feedback vertex set problems

\mathcal{NP}

Linear FPT reductions and computational lower bounds

-hard problems. Well-known examples of such parameterized problems include the vertex cover problem, which is kernelizable to a kernel of size bounded by

An Improved Parameterized Algorithm for the Minimum Node Multiway Cut Problem

2k