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An Efficient Algorithm for the Minimum Clique Partition Problem
, 2000
"... We design an algorithm for an exact solution of the Minimum Clique Partition Problem. For an arbitrary undirected graph G, we use a technique for finite partially ordered sets, in particular, a partition of such sets into the minimum number of paths. The running time of the algorithm is equal to O(n ..."
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We design an algorithm for an exact solution of the Minimum Clique Partition Problem. For an arbitrary undirected graph G, we use a technique for finite partially ordered sets, in particular, a partition of such sets into the minimum number of paths. The running time of the algorithm is equal to O
Minimum clique partition in unit disk graphs
, 2009
"... The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and edges connecting points at distance at most 1. MCP in unit disk ..."
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Cited by 2 (0 self)
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The minimum clique partition (MCP) problem is that of partitioning the vertex set of a given graph into a minimum number of cliques. Given n points in the plane, the corresponding unit disk graph (UDG) has these points as vertices, and edges connecting points at distance at most 1. MCP in unit disk
Maximum Clique and Minimum Clique Partition in Visibility Graphs
, 2000
"... In an alternative approach to "characterizing" the graph class of visibility graphs of simple polygons, we study the problem of finding a maximum clique in the visibility graph of a simple polygon with n vertices. We show that this problem is very hard, if the input polygons are allowe ..."
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In an alternative approach to "characterizing" the graph class of visibility graphs of simple polygons, we study the problem of finding a maximum clique in the visibility graph of a simple polygon with n vertices. We show that this problem is very hard, if the input polygons
A PTAS for Minimum Clique Partition in Unit Disk Graphs
, 2009
"... We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a polynomial time approximation scheme (PTA ..."
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We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a polynomial time approximation scheme
A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs
"... We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time approximat ..."
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We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time
A Weakly Robust PTAS for Minimum Clique Partition in Unit Disk Graphs
"... We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time approximati ..."
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We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NPhard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time
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"... Minimum clique partition in unit disk graphs. (English summary) ..."
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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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package)
"... Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and bas ..."
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Cited by 809 (117 self)
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Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions
Results 1  10
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2,480