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Extensions of the NoThreeInLine Problem
, 2008
"... We investigate generalizations of the NoThreeInLine problem in Z d. For several pairs (k, ℓ) of given positive integers we give algorithmic lower, and upper bounds on the largest sizes of subsets S of points from the ddimensional T × · · · × Tgrid, where no ℓ points in S are contained in a ..."
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We investigate generalizations of the NoThreeInLine problem in Z d. For several pairs (k, ℓ) of given positive integers we give algorithmic lower, and upper bounds on the largest sizes of subsets S of points from the ddimensional T × · · · × Tgrid, where no ℓ points in S are contained in a
Grid drawings of kcolourable graphs
 Vida Dujmović and Attila Pór
"... www.elsevier.com/locate/comgeo It is proved that every kcolourable graph on n vertices has a grid drawing with O(kn) area, and that this bound is best possible. This result can be viewed as a generalisation of the nothreeinline problem. A further area bound is established that includes the aspec ..."
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Cited by 3 (1 self)
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www.elsevier.com/locate/comgeo It is proved that every kcolourable graph on n vertices has a grid drawing with O(kn) area, and that this bound is best possible. This result can be viewed as a generalisation of the nothreeinline problem. A further area bound is established that includes
DOI: 10.1007/s0045300601589 NoThreeinLinein3D 1
"... Abstract. The nothreeinline problem, introduced by Dudeney in 1917, asks for the maximum number of points in the n × n grid with no three points collinear. Erdős proved that the answer is �(n). We consider the analogous problem in three dimensions, and prove that the maximum number of points in t ..."
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Abstract. The nothreeinline problem, introduced by Dudeney in 1917, asks for the maximum number of points in the n × n grid with no three points collinear. Erdős proved that the answer is �(n). We consider the analogous problem in three dimensions, and prove that the maximum number of points
THE NOTHREEINLINE PROBLEM ON A TORUS
"... Abstract. Let T (Zm × Zn) denote the maximal number of points that can be placed on an m × n discrete torus with “no three in a line, ” meaning no three in a coset of a cyclic subgroup of Zm × Zn. By proving upper bounds and providing explicit constructions, for distinct primes p and q, we show that ..."
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Abstract. Let T (Zm × Zn) denote the maximal number of points that can be placed on an m × n discrete torus with “no three in a line, ” meaning no three in a coset of a cyclic subgroup of Zm × Zn. By proving upper bounds and providing explicit constructions, for distinct primes p and q, we show
The Hungarian method for the assignment problem
 Naval Res. Logist. Quart
, 1955
"... Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent in the work ..."
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Cited by 1238 (0 self)
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Assuming that numerical scores are available for the performance of each of n persons on each of n jobs, the "assignment problem" is the quest for an assignment of persons to jobs so that the sum of the n scores so obtained is as large as possible. It is shown that ideas latent
The Extended Linear Complementarity Problem
, 1993
"... We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity of the biline ..."
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Cited by 776 (28 self)
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We consider an extension of the horizontal linear complementarity problem, which we call the extended linear complementarity problem (XLCP). With the aid of a natural bilinear program, we establish various properties of this extended complementarity problem; these include the convexity
Global Optimization with Polynomials and the Problem of Moments
 SIAM Journal on Optimization
, 2001
"... We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear mat ..."
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Cited by 569 (47 self)
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We consider the problem of finding the unconstrained global minimum of a realvalued polynomial p(x) : R R, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear
Cognitive load during problem solving: effects on learning
 COGNITIVE SCIENCE
, 1988
"... Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill. Evidence that conventional problemsolving activity is not effective in schema acquisition is also accumulating. It is suggested t ..."
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Cited by 603 (13 self)
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Considerable evidence indicates that domain specific knowledge in the form of schemes is the primary factor distinguishing experts from novices in problemsolving skill. Evidence that conventional problemsolving activity is not effective in schema acquisition is also accumulating. It is suggested
A New Method for Solving Hard Satisfiability Problems
 AAAI
, 1992
"... We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approac ..."
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Cited by 734 (21 self)
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We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional
Results 1  10
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