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814
Automatic Subspace Clustering of High Dimensional Data
 Data Mining and Knowledge Discovery
, 2005
"... Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, enduser comprehensibility of the results, nonpresumption of any canonical data distribution, and insensitivity to the or ..."
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Cited by 724 (12 self)
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to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
Shape Cliques
, 2007
"... We introduce shape cliques, a simple way to organize a subset of the arrays appearing in an arraylanguagebased application into sets of identically shaped arrays shape cliques and show how a compiler can analyze an application to infer membership in those cliques. We describe an algorithm for pe ..."
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Cited by 1 (0 self)
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We introduce shape cliques, a simple way to organize a subset of the arrays appearing in an arraylanguagebased application into sets of identically shaped arrays shape cliques and show how a compiler can analyze an application to infer membership in those cliques. We describe an algorithm
Clique percolation
, 2008
"... Derényi, Palla and Vicsek introduced the following dependent percolation model, in the context of finding communities in networks. Starting with a random graph G generated by some rule, form an auxiliary graph G ′ whose vertices are the kcliques of G, in which two vertices are joined if the corresp ..."
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Cited by 3 (0 self)
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to the essential global dependence present in G ′. 1 Cliques sharing vertices Fix k ≥ 2 and 1 ≤ ℓ ≤ k − 1. Given a graph G, let Gk,ℓ be the graph whose vertex set is the set of all copies of Kk in G, in which two vertices are adjacent if the corresponding copies of Kk share at least ℓ vertices. Starting from a
Clique Relaxation in . . . .
"... This paper introduces and studies the maximum kplex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graphbased data mining. We establish NPcompleteness of the decision version ..."
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version of the problem on arbitrary graphs. An integer programming formulation is presented and basic polyhedral study of the problem is carried out. A branchandcut implementation is discussed and computational test results on the proposed benchmark instances are also provided.
Clique problem.
"... An inverter for an algorithm A is another algorithm I such that for any y ∈ ranA, the value x = I(y) is a preimage of y s.t. A(x) = y. An inverter for A is optimal if the combined runtime of computing I(y) and verifying A(I(y)) = y is minimal up to a polynomial among all algorithms for this task. ..."
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problem for classical propositional logic, such that A runs in polynomial time if and only if P = NP. Among the applications presented are some results concerning the (conditional) existence or nonexistence of algorithms satisfying other notions of optimality, notably optimal acceptors and optimal proof
Approximating Clique and Biclique Problems
, 1998
"... We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges de ..."
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Cited by 44 (2 self)
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We present here 2approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges
Algorithmic aspects of cliquetransversal and cliqueindependent sets
 DISCRETE APPLIED MATHEMATICS
, 2000
"... A minimum cliquetransversal set MCT (G) of a graph G=(V; E) is a set S V of minimum cardinality that meets all maximal cliques in G. A maximum cliqueindependent set MCI(G) of G is a set of maximum number of pairwise vertexdisjoint maximal cliques. We prove that the problem of nding an MCT (G) and ..."
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Cited by 23 (0 self)
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of Duas et al. (J. Combin. Theory Ser. A 58 (1991) 158{164). We present a polynomial algorithm for the above problems on Helly circulararc graphs which is the first such algorithm for a class of graphs that is not cliqueperfect. We also present polynomial algorithms for the weighted version
Hiding Cliques for Cryptographic Security
 Des. Codes Cryptogr
, 1998
"... We demonstrate how a well studied combinatorial optimization problem may be introduced as a new cryptographic function. The problem in question is that of finding a "large" clique in a random graph. While the largest clique in a random graph is very likely to be of size about 2 log 2 n, it ..."
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Cited by 38 (0 self)
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, it is widely conjectured that no polynomialtime algorithm exists which finds a clique of size (1 + ffl) log 2 n with significant probability for any constant ffl ? 0. We present a very simple method of exploiting this conjecture by "hiding" large cliques in random graphs. In particular, we show
Chordal Graphs and Their Clique Graphs
 IN WG ’95
, 1995
"... In the first part of this paper, a new structure for chordal graph is introduced, namely the clique graph. This structure is shown to be optimal with regard to the set of clique trees. The greedy aspect of the recognition algorithms of chordal graphs is studied. A new greedy algorithm that generali ..."
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Cited by 20 (7 self)
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that generalizes both Maximal cardinality Search (MCS) and Lexicographic Breadth first search is presented. The trace of an execution of MCS is defined and used in two linear time and space algorithms: one builds a clique tree of a chordal graph and the other is a simple recognition procedure of chordal graphs.
Results 1  10
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814