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199
Collective Annotation of Wikipedia Entities in Web Text
"... To take the first step beyond keywordbased search toward entitybased search, suitable token spans (“spots”) on documents must be identified as references to realworld entities from an entity catalog. Several systems have been proposed to link spots on Web pages to entities in Wikipedia. They are ..."
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Cited by 105 (9 self)
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To take the first step beyond keywordbased search toward entitybased search, suitable token spans (“spots”) on documents must be identified as references to realworld entities from an entity catalog. Several systems have been proposed to link spots on Web pages to entities in Wikipedia. They are largely based on local compatibility between the text around the spot and textual metadata associated with the entity. Two recent systems exploit interlabel dependencies, but in limited ways. We propose a general collective disambiguation approach. Our premise is that coherent documents refer to entities from one or a few related topics or domains. We give formulations for the tradeoff between local spottoentity compatibility and measures of global coherence between entities. Optimizing the overall entity assignment is NPhard. We investigate practical solutions based on local hillclimbing, rounding integer linear programs, and preclustering entities followed by local optimization within clusters. In experiments involving over a hundred manuallyannotated Web pages and tens of thousands of spots, our approaches significantly outperform recentlyproposed algorithms.
Survivable network design with degree or order constraints
 SIAM J. ON COMPUTING
, 2009
"... We present algorithmic and hardness results for network design problems with degree or order constraints. The first problem we consider is the Survivable Network Design problem with degree constraints on vertices. The objective is to find a minimum cost subgraph which satisfies connectivity requir ..."
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Cited by 61 (7 self)
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We present algorithmic and hardness results for network design problems with degree or order constraints. The first problem we consider is the Survivable Network Design problem with degree constraints on vertices. The objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds Bv on the vertices. This includes the wellstudied Minimum Bounded Degree Spanning Tree problem as a special case. Our main result is a (2, 2Bv +3)approximation algorithm for the edgeconnectivity Survivable Network Design problem with degree constraints, where the cost of the returned solution is at most twice the cost of an optimum solution (satisfying the degree bounds) and the degree of each vertex v is at most 2Bv + 3. This implies the first constant factor (bicriteria) approximation algorithms for many degree constrained network design problems, including the Minimum Bounded Degree Steiner Forest problem. Our results also extend to directed graphs and provide the first constant factor (bicriteria) approximation algorithms for the Minimum Bounded Degree Arborescence problem and the Minimum Bounded Degree Strongly kEdgeConnected Subgraph problem. In contrast, we show that the vertexconnectivity Survivable Network Design problem with degree constraints is hard to approximate, even when the cost of every edge is zero. A striking aspect of our algorithmic
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
 In 46th Annual IEEE Symposium on Foundations of Computer Science
, 2005
"... At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomialtime algorithm using topolog ..."
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Cited by 56 (15 self)
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At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomialtime algorithm using topological graph theory to decompose a graph into the structure guaranteed by the theorem: a cliquesum of pieces almostembeddable into boundedgenus surfaces. This result has many applications. In particular, we show applications to developing many approximation algorithms, including a 2approximation to graph coloring, constantfactor approximations to treewidth and the largest grid minor, combinatorial polylogarithmicapproximation to halfintegral multicommodity flow, subexponential fixedparameter algorithms, and PTASs for many minimization and maximization problems, on graphs excluding a fixed minor. 1.
Approximation Algorithms for Maximization Problems arising in Graph Partitioning
, 1998
"... Given a graph G = (V; E), a weight function w : E ! R + and a parameter k we examine a family of maximization problems arising naturally when considering a subset U ` V of size exactly k. Specifically we consider the problem of finding a subset U ` V of size k that maximizes : MaxkVertex Cover ..."
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Cited by 55 (5 self)
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Given a graph G = (V; E), a weight function w : E ! R + and a parameter k we examine a family of maximization problems arising naturally when considering a subset U ` V of size exactly k. Specifically we consider the problem of finding a subset U ` V of size k that maximizes : MaxkVertex Cover : the weight of edges incident with vertices in U . MaxkDense Subgraph : the weight of edges in the subgraph induced by U . MaxkCut : the weight of edges cut by the partition (U; V n U ). MaxkNot Cut : the weight of edges not cut by the partition (U; V n U ). We present a number of approximation algorithms based on linear and semidefinite programming, and obtain approximation ratios higher than those previously published.
Pairwise alignment of protein interaction networks
 Journal of Computational Biology
, 2006
"... With an everincreasing amount of available data on protein–protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein–protein interactions ..."
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Cited by 51 (4 self)
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With an everincreasing amount of available data on protein–protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein–protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost. Key words: protein–protein interactions, network alignment, evolutionary models. 1.
The PrizeCollecting Generalized Steiner Tree Problem Via A New Approach Of PrimalDual Schema
"... In this paper we study the prizecollecting version of the Generalized Steiner Tree problem. To the best of our knowledge, there is no general combinatorial technique in approximation algorithms developed to study the prizecollecting versions of various problems. These problems are studied on a cas ..."
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Cited by 45 (13 self)
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In this paper we study the prizecollecting version of the Generalized Steiner Tree problem. To the best of our knowledge, there is no general combinatorial technique in approximation algorithms developed to study the prizecollecting versions of various problems. These problems are studied on a case by case basis by Bienstock et al. [5] by applying an LProunding technique which is not a combinatorial approach. The main contribution of this paper is to introduce a general combinatorial approach towards solving these problems through novel primaldual schema (without any need to solve an LP). We fuse the primaldual schema with Farkas lemma to obtain a combinatorial 3approximation algorithm for the PrizeCollecting Generalized Steiner Tree problem. Our work also inspires a combinatorial algorithm [12] for solving a special case of Kelly’s problem [21] of pricing edges. We also consider the kforest problem, a generalization of kMST and kSteiner tree, and we show that in spite of these problems for which there are constant factor approximation algorithms, the kforest problem is much harder to approximate. In particular, obtaining an approximation factor better than O(n 1/6−ε) for kforest requires substantially new ideas including improving the approximation factor O(n 1/3−ε) for the notorious densest ksubgraph problem. We note that kforest and prizecollecting version of Generalized Steiner Tree are closely related to each other, since the latter is the Lagrangian relaxation of the former.
On finding dense subgraphs
 In ICALP ’09
, 2009
"... Abstract. Given an undirected graph G = (V, E), the density of a subgraph on vertex set S is defined as d(S) = E(S), where E(S) is the set of edges S in the subgraph induced by nodes in S. Finding subgraphs of maximum density is a very well studied problem. One can also generalize this notion t ..."
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Cited by 39 (2 self)
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Abstract. Given an undirected graph G = (V, E), the density of a subgraph on vertex set S is defined as d(S) = E(S), where E(S) is the set of edges S in the subgraph induced by nodes in S. Finding subgraphs of maximum density is a very well studied problem. One can also generalize this notion to directed graphs. For a directed graph one notion of density given by Kannan and Vinay [12] is as follows: given subsets S and T of vertices, the density of the subgraph
Truncated Power Method for Sparse Eigenvalue Problems
"... This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k nonzero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A st ..."
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Cited by 32 (1 self)
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This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most k nonzero components. We propose a simple yet effective solution called truncated power method that can approximately solve the underlying nonconvex optimization problem. A strong sparse recovery result is proved for the truncated power method, and this theory is our key motivation for developing the new algorithm. The proposed method is tested on applications such as sparse principal component analysis and the densest ksubgraph problem. Extensive experiments on several synthetic and realworld data sets demonstrate the competitive empirical performance of our method.
Detecting high logdensities: an O(n1/4) approximation for densest ksubgraph
 In Proc. of the 42nd STOC
, 2010
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Optimal filebundle caching algorithms for datagrids
 in SC ’04: Proceedings of the 2004 ACM/IEEE conference on Supercomputing
"... Abstract The ..."
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