Zsolt Fekete - Profile on Academia.edu (original) (raw)

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Papers by Zsolt Fekete

Research paper thumbnail of Uniform partitioning to bases in a matroid Zsolt Fekete ? and Jácint Szabó ? ?

We say that a matroid M is k-uniform if – provided that it is the disjoint union of its two bases... more We say that a matroid M is k-uniform if – provided that it is the disjoint union of its two bases – for any given k-element subpartition P of its ground set, M can be partitioned into two disjoint bases B1, B2 such that ||B1 ∩ P | − |B2 ∩ P || ≤ 1 for all P ∈ P. The circuit matroid of an undirected graph G is called k-star-uniform if the above holds for all k-element subpartitions containing stars of independent vertices of G. In this paper we prove that the circuit matroids are 1-uniform and 3-star-uniform but not necessarily 2-uniform and 4-star-uniform.

Research paper thumbnail of Uniquely Localizable Networks with Few Anchors

Lecture Notes in Computer Science, 2006

We consider 'source location problems' in undirected graphs motivated by localization problems in... more We consider 'source location problems' in undirected graphs motivated by localization problems in sensor networks. In such a network the fundamental problem is to determine the locations of the sensors in the plane from a subset of pairwise distances. To achieve unique localizability it is necessary to designate a set of sensors, called anchors, for which the exact location is known. We consider the problem of finding a smallest set of anchors which make the network uniquely localizable, provided that the coordinates are 'generic'. We give polynomial time algorithms for two relaxations of the problem. By combining these algorithms we obtain a 2-approximation algorithm for the anchor minimization problem.

Research paper thumbnail of Uniform partitioning to bases in a matroid Zsolt Fekete ? and Jácint Szabó ? ?

We say that a matroid M is k-uniform if – provided that it is the disjoint union of its two bases... more We say that a matroid M is k-uniform if – provided that it is the disjoint union of its two bases – for any given k-element subpartition P of its ground set, M can be partitioned into two disjoint bases B1, B2 such that ||B1 ∩ P | − |B2 ∩ P || ≤ 1 for all P ∈ P. The circuit matroid of an undirected graph G is called k-star-uniform if the above holds for all k-element subpartitions containing stars of independent vertices of G. In this paper we prove that the circuit matroids are 1-uniform and 3-star-uniform but not necessarily 2-uniform and 4-star-uniform.

Research paper thumbnail of Uniquely Localizable Networks with Few Anchors

Lecture Notes in Computer Science, 2006

We consider 'source location problems' in undirected graphs motivated by localization problems in... more We consider 'source location problems' in undirected graphs motivated by localization problems in sensor networks. In such a network the fundamental problem is to determine the locations of the sensors in the plane from a subset of pairwise distances. To achieve unique localizability it is necessary to designate a set of sensors, called anchors, for which the exact location is known. We consider the problem of finding a smallest set of anchors which make the network uniquely localizable, provided that the coordinates are 'generic'. We give polynomial time algorithms for two relaxations of the problem. By combining these algorithms we obtain a 2-approximation algorithm for the anchor minimization problem.

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