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Computing Hereditary Convex Structures

2011
*
Discrete & Computational Geometry
*

More generally, can we quickly

doi:10.1007/s00454-011-9346-8
fatcat:udq7zkbadzdwjkeb7smf7kpnbq
*compute*the blue hull without looking at the whole polytope? This paper considers several instances of*hereditary**computation*and provides new results for them. ... Color red and blue the n vertices of a*convex*polytope P in R 3 . Can we*compute*the*convex*hull of each color class in o(n log n) time? What if we have more than two colors? ... To study the complexity of*hereditary**computing*is part of a broader attempt to understand what makes what hard. ...##
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Computing hereditary convex structures

2009
*
Proceedings of the 25th annual symposium on Computational geometry - SCG '09
*

More generally, can we quickly

doi:10.1145/1542362.1542374
dblp:conf/compgeom/ChazelleM09
fatcat:sre33etsv5e5dczxobeyxg3uiq
*compute*the blue hull without looking at the whole polytope? This paper considers several instances of*hereditary**computation*and provides new results for them. ... Color red and blue the n vertices of a*convex*polytope P in R 3 . Can we*compute*the*convex*hull of each color class in o(n log n) time? What if we have more than two colors? ...*Hereditary*algorithms are nothing new. Given a subset of a simple polygon, Chan [8] showed how to*compute*its*convex*hull in linear time 2 and how to triangulate it in O(n log * n) time. ...##
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LexBFS-orderings of distance-hereditary graphs with application to the diametral pair problem

2000
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Discrete Applied Mathematics
*

As an application we present an algorithm which

doi:10.1016/s0166-218x(99)00157-2
fatcat:q2zg3t4ghffqxin7hqqusiebie
*computes*the diameter and a diametral pair of vertices of a distance-*hereditary*graph in linear time. ? ... Moreover, we characterize those distance-*hereditary*graphs by forbidden subgraphs for which every LexBFS-ordering of the graph is a common perfect elimination ordering of all powers. ... In [15] a tree*structure*for distance-*hereditary*graphs was given, i.e. distance-*hereditary*graphs were characterized as the graphs for which the family of all maximal connected cographs is a dual hypertree ...##
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Guest Editor's Foreword

2011
*
Discrete & Computational Geometry
*

The papers were revised and carefully reviewed according to the high standards of Discrete &

doi:10.1007/s00454-011-9339-7
fatcat:enbn2xpx2bbgpbtlvlsfsum2p4
*Computational*Geometry. ... and deep explorations of the boundaries of Asymptopia, results for the plane and for high-dimensional spaces, and topics ranging from classical*convex*hulls to rigidity theory to topological persistence ... They show that these*hereditary**convex*hull problems can often be solved faster than*computing*the*convex*hull of the subset from scratch. ...##
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Approximating Hereditary Discrepancy via Small Width Ellipsoids
[chapter]

2014
*
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
*

We show that up to this approximation factor, the

doi:10.1137/1.9781611973730.24
dblp:conf/soda/NikolovT15
fatcat:d6yyaykggffrnfvwy647yldmai
*hereditary*discrepancy of a matrix A is characterized by the optimal value of simple geometric*convex*program that seeks to minimize the largest ℓ∞ norm ... Matoušek (2011) showed that this bound is tight up to a polylogarithmic factor, leaving open the question of actually*computing*this bound. ... However, the*structure*and robustness of*hereditary*discrepancy explain its more tractable nature. ...##
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Approximating Hereditary Discrepancy via Small Width Ellipsoids
[article]

2014
*
arXiv
*
pre-print

We show that up to this approximation factor, the

arXiv:1311.6204v2
fatcat:sgoa4xsgyrdc5pvyvnj2jts57a
*hereditary*discrepancy of a matrix A is characterized by the optimal value of simple geometric*convex*program that seeks to minimize the largest ℓ_∞ norm ... Matousek (2011) showed that this bound is tight up to a polylogarithmic factor, leaving open the question of actually*computing*this bound. ... However, the*structure*and robustness of*hereditary*discrepancy explain its more tractable nature. ...##
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LexBFS-orderings and powers of graphs
[chapter]

1997
*
Lecture Notes in Computer Science
*

As an application we get a linear time approximation of the diameter for weak bipolarizable graphs, a subclass of HHD-free graphs containing all chordal graphs, and an algorithm which

doi:10.1007/3-540-62559-3_15
fatcat:gowuukh7ofhnfkqv2c5ctyomue
*computes*the diameter ... and a diametral pair of vertices of a distance-*hereditary*graph in linear time. ... We use the BFS-tree rooted at z which was already*computed*in step (9) . Let b : V -+ IN be the numbering of the vertices of G produced by BFS where b(z) = 1. ...##
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Page 2908 of Mathematical Reviews Vol. , Issue 96e
[page]

1996
*
Mathematical Reviews
*

(E-ZRGZM-SM; Zaragoza)
The order of points on the second

*convex*hull of a simple polygon. (English summary) Discrete*Comput*. Geom. 14 (1995), no. 2, 185-205. ... An analysis is given of s the topological and measure theoretic*structure*of the set F, of farthest points from a given point x on a*convex*surface. ...##
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Induced layered clusters, hereditary mappings, and convex geometries

2002
*
Applied Mathematics Letters
*

This framework appears to be related to order-theoretic concepts of the

doi:10.1016/s0893-9659(01)00133-1
fatcat:x6cjypebhfb7piatqbpfhumzmq
*hereditary*mappings and*convex*geometries, which enables us to give characterizations of those in terms of the monotone linkage functions ... A method for*structural*clustering proposed by the authors is extended to the case when there are externally defined restrictions on the relations between sets and their elements. ... The work was done in the Center for Discrete Mathematics and Theoretical*Computer*Science (DIMACS) at Rutgers University. The authors thank DIMACS' Director Dr. F. Roberts for his support. ...##
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Page 1445 of Mathematical Reviews Vol. , Issue 97C
[page]

1997
*
Mathematical Reviews
*

(English summary) Graph-theoretic concepts in

*computer*science ( Aachen, 1995), 381-395, Lecture Notes in*Comput*. Sci., 1017, Springer, Berlin, 1995. ... An arbitrary finite point set M is divided into*convexity*levels. The first*convexity*level M, contains all the points lying on the boundary of the*convex*hull of M. ...##
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Page 8413 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

Nicolai implies that being distance-

*hereditary*is equivalent to having a certain tree*structure*defined in terms of the maximal complement-reducible (cograph) subgraphs, paralleling the characterization ... “In a companion paper [in Graph-theoretic concepts in*computer*science (Ascona, 1999), 135-147, Springer, Berlin, 1999] we showed that every distance-*hereditary*graph has clique-width at most 3, and a ...##
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A Multi-Objective Unsupervised Feature Selection using Genetic Algorithm

2017
*
International Journal of Science and Research (IJSR)
*

The group feature selection method for the group

doi:10.21275/art20164612
fatcat:ptyqn6pljvf2znr2g5bahikwti
*structure*may be formulated. It performs the task for filtering purpose for group*structure*technique. ... The underlying*structure*has been neglected by the previous feature selection method and it determines the feature separately. ... Gather*structure*is an accumulation of elements. This serves to builds exactness and reductions*computational*time. ...##
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Vertex-Weighted Matching in Two-Directional Orthogonal Ray Graphs
[chapter]

2013
*
Lecture Notes in Computer Science
*

Given such a compact representation of G, and a (possibly negative) weight for each vertex, we show how to

doi:10.1007/978-3-642-45030-3_49
fatcat:ekrg335yazhmnj3ybw6rtuv5su
*compute*a maximum weight matching of G in O(n log 2 n) time. ... As an application of our more general result, we obtain an O(n log 2 n)-time algorithm for*computing*the VCG outcome of a sealed-bid unit-demand auction in which each item has two associated numerical ... Then an MWM of G can be*computed*in O(n log 2 n) time. Proof. Since any two O(1)-word integers can be compared in constant time, we can construct a representation in reps(ξ * , G) in O(n log n) time. ...##
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Rebuilding convex sets in graphs

2005
*
Discrete Mathematics
*

We show that the contour vertices in distance

doi:10.1016/j.disc.2005.03.020
fatcat:6ortapfxm5a33lmya63dngavni
*hereditary*graphs form a geodetic set. ... In this paper we show that every*convex*set of vertices in a graph is the*convex*hull of the collection of its contour vertices. ... Among the wide variety of*structures*that have been studied under abstract*convexity*are metric spaces, ordered sets or lattices and graphs, the last being the focus of this paper. ...##
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Page 3066 of Mathematical Reviews Vol. , Issue 2000d
[page]

2000
*
Mathematical Reviews
*

*Comput*. Oper. Res. 26 (1999), no. 10-11, 1113-1124. ... 2000d:90121 of node-deletion problems for

*hereditary*properties. ...

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