Kao / Li Algorithmic Aspects in Information and Management

Third International Conference, AAIM 2007, Portland, OR, USA, June 6-8, 2007, Proceedings
2007
ISBN: 978-3-540-72870-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 4508, 441 Seiten, eBook

Reihe: Lecture Notes in Computer Science

This book constitutes the refereed proceedings of the Third International Conference on Algorithmic Aspects in Information and Management, AAIM 2007, held in Portland, OR, USA in June 2007.

The 39 revised full papers presented together with abstracts of three invited talks were carefully reviewed and selected from 120 submissions. The papers are organized in topical sections on graph algorithms, combinatorics, scheduling, graph theory, network algorithms, game theory, option theory, computational geometry, graph theory and combinatorics, as well as networks and data.

Written for: Researchers and professionals

Keywords: QoS, Web services, algorithmic mathematics, algorithmics, algorithms, approximation, combinatorial optimization, complexity, computational graph theory, equilibrium computation, game theory, graph theory, heuristics, network algorithms, plane triangulation, randomized algorithms, scheduling.

Zielgruppe

Research

Autoren/Hrsg.

Kao, Ming-Yang

Li, Xiang-Yang

Inhaltsverzeichnis

Contributed Papers To AAIM 2007.- Solving Generalized Maximum Dispersion with Linear Programming.- Significance-Driven Graph Clustering.- An Improved Approximation Algorithm for Maximum Edge 2-Coloring in Simple Graphs.- Digraph Strong Searching: Monotonicity and Complexity.- Algorithms for Counting 2-Sat Solutions and Colorings with Applications.- Collaborative Ranking: An Aggregation Algorithm for Individuals’ Preference Estimation.- A Compact Encoding of Rectangular Drawings with Efficient Query Supports.- A New Efficient Algorithm for Computing the Longest Common Subsequence.- Scheduling a Flexible Batching Machine.- Global Search Method for Parallel Machine Scheduling.- Releasing and Scheduling of Lots in a Wafer Fab.- Mixed Criteria Packet Scheduling.- Efficient Algorithms for k-Disjoint Paths Problems on DAGs.- Acyclic Edge Colouring of Outerplanar Graphs.- Smallest Bipartite Bridge-Connectivity Augmentation (Extended Abstract).- Approximation Algorithms for the Graph Orientation Minimizing the Maximum Weighted Outdegree.- An Efficient Algorithm for the Evacuation Problem in a Certain Class of a Network with Uniform Path-Lengths.- Online OVSF Code Assignment with Resource Augmentation.- Optimal Joint Rate and Power Allocation in CDMA Networks.- Suppressing Maximum Burst Size Throughout the Path with Non-work Conserving Schedulers.- How to Play the Majority Game with Liars.- On Satisfiability Games and the Power of Congestion Games.- The Complexity of Algorithms Computing Game Trees on Random Assignments.- An Efficient, and Fast Convergent Algorithm for Barrier Options.- An Ingenious, Piecewise Linear Interpolation Algorithm for Pricing Arithmetic Average Options.- Optimal Order Allocation with Discount Pricing.- Convex Hulls of Point-Sets and Non-uniformHypergraphs.- Optimal st-Orientations for Plane Triangulations.- Minimum Spanning Tree with Neighborhoods.- An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem.- Optimal Field Splitting with Feathering in Intensity-Modulated Radiation Therapy.- Approximating the Maximum Independent Set and Minimum Vertex Coloring on Box Graphs.- BMA *: An Efficient Algorithm for the One-to-Some Shortest Path Problem on Road Maps.- Strip Packing vs. Bin Packing.- Probe Matrix Problems: Totally Balanced Matrices.- Efficiency of Data Distribution in BitTorrent-Like Systems.- Design of a Fuzzy PI Controller to Guarantee Proportional Delay Differentiation on Web Servers.- Improved Approximation Algorithms for Predicting RNA Secondary Structures with Arbitrary Pseudoknots.- A Heuristic Method for Selecting Support Features from Large Datasets.- Invited Lecture.- Game and Market Equilibria: Computation, Approximation, and Smoothed Analysis.- Ad Auctions – Current and Future Research.- Expressive Commerce and Its Application to Sourcing: How We Conducted $25 Billion of Generalized Combinatorial Auctions.

Leseproben

Significance-Driven Graph Clustering (p. 11-12)

Marco Gaertler, Robert G¨orke, and Dorothea Wagner
Faculty of Informatics, Universit¨at Karlsruhe (TH)

Abstract. Modularity, the recently defined quality measure for clusterings, has attained instant popularity in the fields of social and natural sciences. We revisit the rationale behind the definition of modularity and explore the founding paradigm. This paradigm is based on the trade-off between the achieved quality and the expected quality of a clustering with respect to networks with similar intrinsic structure. We experimentally evaluate realizations of this paradigm systematically, including modularity, and describe efficient algorithms for their optimization. We confirm the feasibility of the resulting generality by a first systematic analysis of the behavior of these realizations on both artificial and on real-world data, arriving at remarkably good results of community detection.

1 Introduction

Discovering natural groups and large scale inhomogeneities is a crucial task in the exploration and analysis of large and complex networks. This task is usually realized with clustering methods. The majority of algorithms for graph clustering are based on the paradigm of intra-cluster density versus inter-cluster sparsity. Several formalizations have been proposed and evaluated, an overview of such techniques is given in [1]. Recently, Girvan and Newman [2] proposed the objective function modularity, which indirectly incorporates this paradigm. Modularity evaluates a clustering based on the fraction of intra-cluster edges compared to the expected value of this number. Modularity was .rst introduced as a quality measure of a clustering, however, a simple greedy algorithm, solely based on modularity, has been proposed shortly after by Newman [3]. The definition of modularity and this algorithm evoked a surge of interest, yielding many studies concerning different applications, such as protein interaction dependencies, recommendation systems or social network analysis, and possible adjustments (see e.g. [4,5,6,7]). Moreover, a range of alternative algorithmic approaches has been proposed, based on a greedy agglomeration [8,9], on spectral division [10,11], simulated annealing [12,13] and extremal optimization [14]. Recently, it has been proven, that it is NP-hard to optimize modularity [15], which justi.es the need for heuristics and approximations. Note that little is known on the approximability of modularity.

However, to our knowledge, no systematic evaluation of modularity-based clustering has been performed, yet. In this work, we conduct such an evaluation and, additionally, we advance towards a profound understanding of the rationales modularity is based upon. We formally state and investigate the generalized founding paradigm for the signi.cance of a clustering as the trade-off between the achieved quality and the expected quality for random networks incorporating the intrinsic properties of the original network. We experimentally evaluate realizations of this paradigm (including modularity itself) and extensively evaluate algorithms that each optimize a realization, followed by a partial discussion of their behavior. Furthermore, we present an algorithm that efficiently optimizes the particularly promising realization relative performance signi.cance in O(n2 log n) time. We compare the performance of these algorithms in terms of clustering quality to that of other clustering algorithms, on a set of random pre-clustered graphs and complement our findings with results on real data. Our results indicate the feasibility of the paradigm in that, on the whole, our algorithms surpass the benchmark algorithms, and in that the generality of the approach is justified by specific realizations excelling on real-world data.

This paper is organized as follows: After introducing the necessary preliminaries for graph clustering and some quality measures (Sec. 2), we give the formal definition of our significance paradigm and present some realizations (Sec. 3). Section 4 scrutinizes the greedy algorithms which are employed to obtain clusterings with high signi.cance score, including an e.cient implementation for a quick divisive merge. The setup and the results of the experimental evaluation are described in Section 5 which are followed by a conclusion.