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776
A simple proof that ANDcompression of NPcomplete problems is hard
 Electronic Colloquium on Computational Complexity (ECCC), 2014. Available at http://eccc.hpiweb.de/report/2014/075
"... Drucker [1] proved the following result: Unless the unlikely complexitytheoretic collapse coNP ⊆ NP/poly occurs, there is no ANDcompression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NPcomplete parameterized problems. We present a simple p ..."
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Cited by 2 (0 self)
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Drucker [1] proved the following result: Unless the unlikely complexitytheoretic collapse coNP ⊆ NP/poly occurs, there is no ANDcompression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NPcomplete parameterized problems. We present a simple
Training a 3Node Neural Network is NPComplete
, 1992
"... We consider a 2layer, 3node, ninput neural network whose nodes compute linear threshold functions of their inputs. We show that it is NPcomplete to decide whether there exist weights and thresholds for this network so that it produces output consistent with a given set of training examples. We ..."
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Cited by 231 (3 self)
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We consider a 2layer, 3node, ninput neural network whose nodes compute linear threshold functions of their inputs. We show that it is NPcomplete to decide whether there exist weights and thresholds for this network so that it produces output consistent with a given set of training examples. We
Some NPcomplete Geometric Problems
"... We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard i ..."
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Cited by 98 (1 self)
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We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard
System BV is NPcomplete
, 2005
"... System BV is an extension of multiplicative linear logic (MLL) with the rules mix, nullary mix, and a selfdual, noncommutative logical operator, called seq. While the rules mix and nullary mix extend the deductive system, the operator seq extends the language of MLL. Due to the operator seq, syste ..."
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Cited by 11 (4 self)
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is NPcomplete by encoding the 3Partition problem in FBV. I provide a simple completeness proof of this encoding by resorting to a novel proof theoretical method for reducing the nondeterminism in proof search, which is also of independent interest.
OneinTwoMatching Problem is NPcomplete
, 2006
"... 2dimensional Matching Problem, which requires to find a matching of left to rightvertices in a balanced 2nvertex bipartite graph, is a wellknown polynomial problem, while various variants, like the 3dimensional analogoue (3DM, with triangles on a tripartite graph), or the Hamiltonian Circuit P ..."
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and Travelling Salesman Problem being NPcomplete. In this paper we show that a small modification of the 2dimensional Matching and Assignment Problems in which for each i ≤ n/2 it is required that either π(2i − 1) = 2i − 1 or π(2i) = 2i, is a NPcomplete problem. The proof is by linear reduction from SAT (or
Some NPcomplete Geometric Problems
 In 8th ACM Symposium on Theory of Computing, STOC
, 1976
"... We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard if ..."
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Cited by 1 (1 self)
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We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NPcomplete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NPhard
Shortest anisotropic paths with few bends is NPcomplete
 The 18th Fall Workshop on Computational Geometry
, 2008
"... In the shortest anisotropic path (SAP) problem [7], the goal is to minimize the weighted length of a path on a triangulated terrain, where the weight of a path segment ab depends both on the face containing ab and the direction of ab. The problem is a generalization of the weighted region problem. ..."
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Cited by 2 (2 self)
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if there exists a SAP of length at most L that has at most k bends is NPcomplete. Our proof uses a reduction from 3SAT following the idea of Canny and Reif’s hardness result [2] for shortest paths among obstacles in 3D, though our gadgets are different as our paths lie on a 2D surface. Our problem is a
The hardness of the Lemmings game, or Oh no, more NPcompleteness proofs
 In Proceedings of the 3rd International Conference on Fun with Algorithms
, 2004
"... In the computer game ‘Lemmings’, the player must guide a tribe of greenhaired Lemming creatures to safety, and hence save them from an untimely demise. We formulate the decision problem which is, given a level of the game, to decide whether it is possible to complete the level (and hence to find a ..."
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Cited by 10 (0 self)
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In the computer game ‘Lemmings’, the player must guide a tribe of greenhaired Lemming creatures to safety, and hence save them from an untimely demise. We formulate the decision problem which is, given a level of the game, to decide whether it is possible to complete the level (and hence to find a
The Rectilinear Steiner Arborescence Problem is NPComplete
, 2000
"... Given a set P of points in the first quadrant, a Rectilinear Steiner Arborescence (RSA) is a directed tree rooted at the origin, containing all points in P , and composed solely of horizontal and vertical edges oriented from left to right, or from bottom to top. The complexity of finding an RSA with ..."
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Cited by 28 (0 self)
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with the minimum total edge length for general planar point sets has been a major open problem, and has important applications in VLSI. In this paper, we prove the problem is strongly NPcomplete. The proof also shows the Euclidean version of the Steiner Arborescence problem is NPhard.
ZigZag Numberlink is NPComplete
, 2014
"... When can t terminal pairs in an m × n grid be connected by t vertexdisjoint paths that cover all vertices of the grid? We prove that this problem is NPcomplete. Our hardness result can be compared to two previous NPhardness proofs: Lynch’s 1975 proof without the “cover all vertices” constraint, a ..."
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When can t terminal pairs in an m × n grid be connected by t vertexdisjoint paths that cover all vertices of the grid? We prove that this problem is NPcomplete. Our hardness result can be compared to two previous NPhardness proofs: Lynch’s 1975 proof without the “cover all vertices” constraint
Results 1  10
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776