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Computing Hereditary Convex Structures
2011
Discrete & Computational Geometry
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More generally, can we quickly 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. ...
doi:10.1007/s00454-011-9346-8
fatcat:udq7zkbadzdwjkeb7smf7kpnbq
Computing hereditary convex structures
2009
Proceedings of the 25th annual symposium on Computational geometry - SCG '09
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More generally, can we quickly 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. ...
doi:10.1145/1542362.1542374
dblp:conf/compgeom/ChazelleM09
fatcat:sre33etsv5e5dczxobeyxg3uiq
LexBFS-orderings of distance-hereditary graphs with application to the diametral pair problem
2000
Discrete Applied Mathematics
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As an application we present an algorithm which 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 ...
doi:10.1016/s0166-218x(99)00157-2
fatcat:q2zg3t4ghffqxin7hqqusiebie
Guest Editor's Foreword
2011
Discrete & Computational Geometry
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The papers were revised and carefully reviewed according to the high standards of Discrete & 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. ...
doi:10.1007/s00454-011-9339-7
fatcat:enbn2xpx2bbgpbtlvlsfsum2p4
Approximating Hereditary Discrepancy via Small Width Ellipsoids
[chapter]
2014
Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms
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We show that up to this approximation factor, the 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. ...
doi:10.1137/1.9781611973730.24
dblp:conf/soda/NikolovT15
fatcat:d6yyaykggffrnfvwy647yldmai
Approximating Hereditary Discrepancy via Small Width Ellipsoids
[article]
2014
arXiv
pre-print
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We show that up to this approximation factor, the 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. ...
arXiv:1311.6204v2
fatcat:sgoa4xsgyrdc5pvyvnj2jts57a
LexBFS-orderings and powers of graphs
[chapter]
1997
Lecture Notes in Computer Science
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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 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. ...
doi:10.1007/3-540-62559-3_15
fatcat:gowuukh7ofhnfkqv2c5ctyomue
Page 2908 of Mathematical Reviews Vol. , Issue 96e
[page]
1996
Mathematical Reviews
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(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. ...
Induced layered clusters, hereditary mappings, and convex geometries
2002
Applied Mathematics Letters
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This framework appears to be related to order-theoretic concepts of the 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. ...
doi:10.1016/s0893-9659(01)00133-1
fatcat:x6cjypebhfb7piatqbpfhumzmq
Page 1445 of Mathematical Reviews Vol. , Issue 97C
[page]
1997
Mathematical Reviews
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(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. ...
Page 8413 of Mathematical Reviews Vol. , Issue 2000m
[page]
2000
Mathematical Reviews
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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 ...
A Multi-Objective Unsupervised Feature Selection using Genetic Algorithm
2017
International Journal of Science and Research (IJSR)
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The group feature selection method for the group 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. ...
doi:10.21275/art20164612
fatcat:ptyqn6pljvf2znr2g5bahikwti
Vertex-Weighted Matching in Two-Directional Orthogonal Ray Graphs
[chapter]
2013
Lecture Notes in Computer Science
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Given such a compact representation of G, and a (possibly negative) weight for each vertex, we show how to 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. ...
doi:10.1007/978-3-642-45030-3_49
fatcat:ekrg335yazhmnj3ybw6rtuv5su
Rebuilding convex sets in graphs
2005
Discrete Mathematics
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We show that the contour vertices in distance 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. ...
doi:10.1016/j.disc.2005.03.020
fatcat:6ortapfxm5a33lmya63dngavni
Page 3066 of Mathematical Reviews Vol. , Issue 2000d
[page]
2000
Mathematical Reviews
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Comput. Oper. Res. 26 (1999), no. 10-11, 1113-1124. ...
2000d:90121
of node-deletion problems for hereditary properties. ...
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