Results 11  20
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18,309
Lineartime algorithms to color topological graphs
, 2005
"... We describe a lineartime algorithm for 4coloring planar graphs. We indeed give an O(V + E + χ  + 1)time algorithm to Ccolor Vvertex Eedge graphs embeddable on a 2manifold M of Euler characteristic χ where C(M) is given by Heawood’s (minimax optimal) formula. Also we show how, in O(V + E) ..."
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We describe a lineartime algorithm for 4coloring planar graphs. We indeed give an O(V + E + χ  + 1)time algorithm to Ccolor Vvertex Eedge graphs embeddable on a 2manifold M of Euler characteristic χ where C(M) is given by Heawood’s (minimax optimal) formula. Also we show how, in O(V + E
Some LinearTime Algorithms for Systolic Arrays
"... We survey some recent results on lineartime algorithms for systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for the GCD of two nbit binar ..."
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Cited by 12 (7 self)
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We survey some recent results on lineartime algorithms for systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for the GCD of two n
Lineartime algorithms for proportional contact graph representations
, 2011
"... Abstract. In a proportional contact representation of a planar graph, each vertex is represented by a simple polygon with area proportional to a given weight, and edges are represented by adjacencies between the corresponding pairs of polygons. In this paper we study proportional contact representat ..."
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Cited by 3 (2 self)
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and runs in time. We also describe a lineartime algorithm for proportional contact representation of planar 3trees with 8sided rectilinear polygons and show that this optimal, as there exist planar 3trees that requires 8sided polygons. Finally, we show that a maximal outerplanar graph admits a
Some LinearTime Algorithms for Systolic Arrays
, 2000
"... We survey some recent results on lineartime algorithms for systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for the GCD of two nbit binar ..."
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We survey some recent results on lineartime algorithms for systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for the GCD of two n
Some LinearTime Algorithms for Systolic Arrays*
"... Abstract We survey some recent results on lineartime algorithms for systolic arrays. In particular, weshow how the greatest common divisor (GCD) of two polynomials of degree n over a finitefield can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for theGCD of two nbit ..."
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Abstract We survey some recent results on lineartime algorithms for systolic arrays. In particular, weshow how the greatest common divisor (GCD) of two polynomials of degree n over a finitefield can be computed in time O(n) on a linear systolic array of O(n) cells; similarly for theGCD of two n
A Linear Time Algorithm for Tree Mapping
 Arbeitspapiere der GMD No. 1046, St
, 1996
"... this paper we present a linear time algorithm for a tree mapping measure. This improvement makes the processing of large gene and species trees possible as they may arise in the study of large gene families. ..."
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Cited by 6 (1 self)
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this paper we present a linear time algorithm for a tree mapping measure. This improvement makes the processing of large gene and species trees possible as they may arise in the study of large gene families.
Linear Time Algorithm for Projective Clustering
"... Abstract. Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points P in Rd space, projective clustering is to find a set F of k lower dimensional jflats so that the average distance (or squar ..."
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for this challenging problem and achieve linear time solutions for three cases, general projective clustering, regular projective clustering, and Lτ sense projective clustering. For the general projective clustering problem, we show that for any given small numbers 0 < γ, < 1, our approach first removes γ
LinearTime Algorithms for Finding Tucker Submatrices and LekkerkerkerBoland Subgraphs
, 2013
"... Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a lineartime algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of binary matrices that do not have the cons ..."
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Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a lineartime algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of binary matrices that do not have
Lineartime algorithms for pairwise statistical problems
 In Proc. of NIPS
, 2010
"... Several key computational bottlenecks in machine learning involve pairwise distance computations, including allnearestneighbors (finding the nearest neighbor(s) for each point, e.g. in manifold learning) and kernel summations (e.g. in kernel density estimation or kernel machines). We consider the ..."
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Cited by 16 (7 self)
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the general, bichromatic case for these problems, in addition to the scientific problem of Nbody simulation. In this paper we show for the first timeO(
Results 11  20
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18,309