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96
SDP gaps and UGChardness for MaxCutGain
, 2008
"... Given a graph with maximum cut of (fractional) size c, the Goemans–Williamson semidefinite programming (SDP)based algorithm is guaranteed to find a cut of size at least.878 · c. However this guarantee becomes trivial when c is near 1/2, since making random cuts guarantees a cut of size 1/2 (i.e., ..."
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Cited by 26 (3 self)
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. This implies that beating the CharikarWirth guarantee with any efficient algorithm is NPhard, assuming the Unique Games Conjecture (UGC). This result essentially settles the asymptotic approximability of MaxCut, assuming UGC. Building on the first contribution, we show how “randomness reduction ” on related
Clustering with qualitative information
 In Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
, 2003
"... We consider the problem of clustering a collection of elements based on pairwise judgments of similarity and dissimilarity. Bansal, Blum and Chawla [1] cast the problem thus: given a graph G whose edges are labeled “+ ” (similar) or “− ” (dissimilar), partition the vertices into clusters so that ..."
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Cited by 123 (9 self)
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We consider the problem of clustering a collection of elements based on pairwise judgments of similarity and dissimilarity. Bansal, Blum and Chawla [1] cast the problem thus: given a graph G whose edges are labeled “+ ” (similar) or “− ” (dissimilar), partition the vertices into clusters so that the number of pairs correctly (resp. incorrectly) classified with respect to the input labeling is maximized (resp. minimized). Complete graphs, where the classifier labels every edge, and general graphs, where some edges are not labeled, are both worth studying. We answer several questions left open in [1] and provide a sound overview of clustering with qualitative information. We give a factor 4 approximation for minimization on complete graphs, and a factor O(log n) approximation for general graphs. For the maximization version, a PTAS for complete graphs is shown in [1]; we give a factor 0.7664 approximation for general graphs, noting that a PTAS is unlikely by proving APXhardness. We also prove the APXhardness of minimization on complete graphs. 1.
Information extraction
 FnT Databases
"... The automatic extraction of information from unstructured sources has opened up new avenues for querying, organizing, and analyzing data by drawing upon the clean semantics of structured databases and the abundance of unstructured data. The field of information extraction has its genesis in the natu ..."
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Cited by 90 (4 self)
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The automatic extraction of information from unstructured sources has opened up new avenues for querying, organizing, and analyzing data by drawing upon the clean semantics of structured databases and the abundance of unstructured data. The field of information extraction has its genesis in the natural language processing community where the primary impetus came from competitions centered around the recognition of named entities like people names and organization from news articles. As society became more data oriented with easy online access to both structured and unstructured data, new applications of structure extraction came around. Now, there is interest in converting our personal desktops to structured databases, the knowledge in scientific publications to structured records, and harnessing the Internet for structured fact finding queries. Consequently, there are many different communities of researchers bringing in techniques from machine learning, databases, information retrieval, and computational linguistics for various aspects of the information extraction problem. This review is a survey of information extraction research of over two decades from these diverse communities. We create a taxonomy of the field along various dimensions derived from the nature of theextraction task, the techniques used for extraction, the variety of input resources exploited, and the type of output produced. We elaborate on rulebased and statistical methods for entity and relationship extraction. In each case we highlight the different kinds of models for capturing the diversity of clues driving the recognition process and the algorithms for training and efficiently deploying the models. We survey techniques for optimizing the various steps in an information extraction pipeline, adapting to dynamic data, integrating with existing entities and handling uncertainty in the extraction process. 1
unknown title
"... Maximizing quadratic programs:extending Grothendieck's inequality Moses Charikar*Princeton University Anthony Wirth#Princeton University Abstract This paper considers the following type of quadratic programming problem. Given an arbitrary matrix A, whose diagonal elements are zero, find x 2 { ..."
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Maximizing quadratic programs:extending Grothendieck's inequality Moses Charikar*Princeton University Anthony Wirth#Princeton University Abstract This paper considers the following type of quadratic programming problem. Given an arbitrary matrix A, whose diagonal elements are zero, find x 2
Lower bounds for Grothendieck problems
"... Given a graph G = (V;E), consider the following problem: The input is a function A: E! R, and the goal is to maximize P (u;v)2E A(u; v)f(u)f(v) over all functions f: V! f¡1; 1g. This problem was formalized by Alon, Makarychev, Makarychev and Naor [AMMN05]; it is a weighted version of the 2cluster \ ..."
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Cited by 1 (0 self)
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hardness result at versus ( = log(1=)) for any constant > 0. This matches the SDP algorithm of Charikar and Wirth [CW04]. Our lower bounds in the bipartite KN;N hold even in the case of CutNorm for zerosum matrices; we show how to translate the best known lower bound on Grothendieck's constant (due
ModularityMaximizing Graph Communities via Mathematical Programming
"... In many networks, it is of great interest to identify communities, unusually densely knit groups of individuals. Such communities often shed light on the function of the networks or underlying properties of the individuals. Recently, Newman suggested modularity as a natural measure of the quality ..."
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Cited by 37 (1 self)
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two novel algorithms. More specifically, the algorithms round solutions to linear and vector programs. Importantly, the linear programing algorithm comes with an a posteriori approximation guarantee: by comparing the solution quality to the fractional solution of the linear program, a bound
On the RedBlue Set Cover Problem
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms
, 2000
"... Given a finite set of "red" elements R, a finite set of "blue" elements B and a family S ` 2 R[B , the redblue set cover problem is to find a subfamily C ` S which covers all blue elements, but which covers the minimum possible number of red elements. We note that RedBlue Se ..."
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Cited by 48 (0 self)
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Given a finite set of "red" elements R, a finite set of "blue" elements B and a family S ` 2 R[B , the redblue set cover problem is to find a subfamily C ` S which covers all blue elements, but which covers the minimum possible number of red elements. We note that RedBlue Set Cover is closely related to several combinatorial optimization problems studied earlier. These include the group Steiner problem, directed Steiner problem, minimum label path, minimum monotone satisfying assignment and symmetric label cover. From the equivalence of RedBlue Set Cover and MMSA3 it follows that, unless P=NP, even the restriction of RedBlue Set Cover where every set contains only one blue and two red elements cannot be approximated to within O(2 log 1\Gammaffi n ) , where ffi = 1= log log c n, for any constant c ! 1=2 (where n = S). We give integer programming formulations of the problem and use them to obtain a 2 p n approximation algorithm for the restricted case of RedBlue Set Cove...
On Approximating Complex Quadratic Optimization Problems Via Semidefinite Programming Relaxations
 Mathematical Programming, Series B
, 2007
"... Abstract. In this paper we study semidefinite programming (SDP) models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian form. These problems capture a class of well–known combinatorial optimization problems, as well as problems in control theory. For i ..."
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Cited by 28 (4 self)
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. For instance, they include Max–3–Cut with arbitrary edge weights (i.e. some of the edge weights might be negative). We present a generic algorithm and a unified analysis of the SDP relaxations which allow us to obtain good approximation guarantees for our models. Specifically, we give an (k sin(pi/k))2/(4pi
Deterministic pivoting algorithms for constrained ranking and Clustering Problems
, 2007
"... We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon, Charikar, and Newman [4], Ailon and Charikar [3], ..."
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Cited by 32 (4 self)
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We consider ranking and clustering problems related to the aggregation of inconsistent information, in particular, rank aggregation, (weighted) feedback arc set in tournaments, consensus and correlation clustering, and hierarchical clustering. Ailon, Charikar, and Newman [4], Ailon and Charikar [3
Nearoptimal algorithms for maximum constraint satisfaction problems
 In SODA ’07: Proceedings of the eighteenth annual ACMSIAM symposium on Discrete algorithms
, 2007
"... In this paper we present approximation algorithms for the maximum constraint satisfaction problem with k variables in each constraint (MAX kCSP). Given a (1 − ε) satisfiable 2CSP our first algorithm finds an assignment of variables satisfying a 1 − O ( √ ε) fraction of all constraints. The best pr ..."
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Cited by 20 (3 self)
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previously known result, due to Zwick, was 1 − O(ε 1/3). The second algorithm finds a ck/2 k approximation for the MAX kCSP problem (where c> 0.44 is an absolute constant). This result improves the previously best known algorithm by Hast, which had an approximation guarantee of Ω(k/(2 k log k)). Both
Results 1  10
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96