Results 1  10
of
856
Hellytype theorems and generalized linear programming
 DISCRETE COMPUT. GEOM
, 1994
"... This thesis establishes a connection between the Helly theorems, a collection of results from combinatorial geometry, and the class of problems which we call Generalized Linear Programming, or GLP, which can be solved by combinatorial linear programming algorithms like the simplex method. We use the ..."
Abstract

Cited by 61 (0 self)
 Add to MetaCart
This thesis establishes a connection between the Helly theorems, a collection of results from combinatorial geometry, and the class of problems which we call Generalized Linear Programming, or GLP, which can be solved by combinatorial linear programming algorithms like the simplex method. We use
A Topological Colorful Helly Theorem
, 2003
"... Abstract Let F1; : : : ; Fd+1 be d+1 families of convex sets in Rd. The Colorful Helly Theorem (see [3]) asserts that if T d+1 i=1 Fi 6 = ; for all choices ofF 1 2 F1; : : : ; Fd+1 2 Fd+1 then there exists an 1 ^ i ^ d + 1 such thatT F 2Fi F 6 =;.Our main result is both a topological and a matroidal ..."
Abstract
 Add to MetaCart
matroidal extension of the colorful Helly theorem. A simplicial complex X is dLeray if Hi(Y; Q) = 0 for all induced subcomplexes Y ae X and i * d. Theorem: Let X be a dLeray complex on the vertex set V. Suppose M is a matroidal complex on the same vertex set V with rank function ae. If M ae X
BicliqueHelly graphs
 GRAPHS AND COMBINATORICS
, 2007
"... A graph is bicliqueHelly when its family of (maximal) bicliques is a Helly family. We describe characterizations for bicliqueHelly graphs, leading to polynomial time recognition algorithms. In addition, we relate bicliqueHelly graphs to the classes of cliqueHelly, diskHelly and neighborhoodHel ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
A graph is bicliqueHelly when its family of (maximal) bicliques is a Helly family. We describe characterizations for bicliqueHelly graphs, leading to polynomial time recognition algorithms. In addition, we relate bicliqueHelly graphs to the classes of cliqueHelly, diskHelly and neighborhoodHelly
On the power of discrete and lexicographic Hellytype theorems
 In Proc. 46th IEEE Sympos. Foundat. Comput. Sci. (FOCS
, 2004
"... Abstract Helly's theorem says that if every d + 1 elements of agiven finite set of convex objects in IR d have a common point, then there is a point common to all of the objectsin the set. We define three new types of Helly theorems: discrete Helly theorems where the common point shouldbelong ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
new discrete and lexicographicHelly numbers. Using these new types of Helly theorems we get linear time solutions for various optimization problems. For this, we define a new framework, DLPtype (Discrete Linear Programming type), and provide new algorithms that solve in randomized linear time fixed
On hereditary Helly classes of graphs
 DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 2008
"... In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of cliqueHelly, diskHelly, bicliqueHelly, neighbourhoodHelly graphs, respectively. A natural question is to determine for which graphs the corre ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of cliqueHelly, diskHelly, bicliqueHelly, neighbourhoodHelly graphs, respectively. A natural question is to determine for which graphs
Helly Numbers of Polyominoes
"... We define the Helly number of a polyomino P as the smallest number h such that the hHelly property holds for the family of symmetric and translated copies of P on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist any ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We define the Helly number of a polyomino P as the smallest number h such that the hHelly property holds for the family of symmetric and translated copies of P on the integer grid. We prove the following: (i) the only polyominoes with Helly number 2 are the rectangles, (ii) there does not exist
Computational aspects of the helly property: a survey
 Journal of the Brazilian Computer Society
"... In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. Say that a family of subsets has the Helly property when every subfamily of it, formed by pairwise intersecting subsets, contains a common element. There are many generalizations of this propert ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. Say that a family of subsets has the Helly property when every subfamily of it, formed by pairwise intersecting subsets, contains a common element. There are many generalizations
Complexity Aspects of the Helly Property: Graphs and Hypergraphs
, 2009
"... In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. A family of subsets has the Helly property when every subfamily thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations of this property exist which are r ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
In 1923, Eduard Helly published his celebrated theorem, which originated the well known Helly property. A family of subsets has the Helly property when every subfamily thereof, formed by pairwise intersecting subsets, contains a common element. Many generalizations of this property exist which
Helly CircularArc Graph Isomorphism Is in Logspace
"... Abstract. We present logspace algorithms for the canonical labeling problem and the representation problem of Helly circulararc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Δ trees employed in McConnell ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We present logspace algorithms for the canonical labeling problem and the representation problem of Helly circulararc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Δ trees employed in Mc
Results 1  10
of
856