Feodor Dragan - Academia.edu (original) (raw)

Papers by Feodor Dragan

Research paper thumbnail of On the Minimum Eccentricity Shortest Path Problem

Lecture Notes in Computer Science, 2015

Research paper thumbnail of Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs

Proceedings of the Twenty Fourth Annual Symposium on Computational Geometry, Jun 9, 2008

Research paper thumbnail of Discrete Applied Mathematics 98 (2000) 191--207

ABSTRACT For an undirected graph G the kth power G of G is the graph with the same vertex set as ... more ABSTRACT For an undirected graph G the kth power G of G is the graph with the same vertex set as G where two vertices are adjacent i# their distance is at most k in G. In this paper we prove that every LexBFS-ordering of a distance-hereditary graph is both a common perfect elimination ordering of all even powers and a common semi-simplicial ordering of all powers of this graph. 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. 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. ? 2000 Elsevier Science B.V. All rights reserved.

Research paper thumbnail of Provably Good Global Buffering by Generalized

Research paper thumbnail of Generalized Powers of Graphs and Their Algorithmic Use

Lecture Notes in Computer Science, 2006

Research paper thumbnail of The Algorithmic Use of Hypertree Structure and Maximum Neighbourhood Orderings

Proceedings of the 20th International Workshop on Graph Theoretic Concepts in Computer Science, Jun 16, 1994

Research paper thumbnail of Navigating in a Graph by Aid of Its Spanning Tree Metric

Siam Journal on Discrete Mathematics, 2011

Research paper thumbnail of Homogeneously orderable graphs and the Steiner tree problem

Lecture Notes in Computer Science, 1995

ABSTRACT In this paper we introduce homogeneously orderable graphs which are a common generalizat... more ABSTRACT In this paper we introduce homogeneously orderable graphs which are a common generalization of distance-hereditary graphs, dually chordal graphs and homogeneous graphs. We present a characterization of the new class in terms of a tree structure of the closed neighbourhoods of homogeneous sets in 2-graphs which is closely related to the defining elimination ordering.

Research paper thumbnail of LexBFS-orderings and powers of graphs

Lecture Notes in Computer Science, 1997

For an undirected graph G the k-th power G k of G is the graph with the same vertex set as G wher... more For an undirected graph G the k-th power G k of G is the graph with the same vertex set as G where two vertices are adjacent iff their distance is at most k in G. In this paper we consider LexBFS-orderings of chordal, distance-hereditaxy and HHD-free graphs (the graphs where each cycle of length at least five has two chords) with respect to their powers. We show that any LexBFS-ordering of a chordal graph is a common perfect elimination ordering of all odd powers of this graph, and any LexBFS-ordering of a distance-hereditary graph is a common perfect elimination ordering of all its even powers. It is wellknown that any LexBFS-ordering of a HHD-free graph is a so-called semi-simplicial ordering. We show, that any LexBFS-ordering of a HHD-free graph is a common semi-simplicial ordering of all its odd powers. Moreover we characterize those chordal, distance-hereditary and HHD-free graphs by forbidden isometric subgraphs for which any LexBFS-ordering of the graph is a common perfect elimination ordering of all its nontrivial powers. 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.

Research paper thumbnail of Effective network monitoring

Proceedings. 13th International Conference on Computer Communications and Networks (IEEE Cat. No.04EX969), 2004

Research paper thumbnail of A linear-time algorithm for finding a central vertex of a chordal graph

Lecture Notes in Computer Science, 1994

Research paper thumbnail of On condorcet and median points of simple rectilinear polygons

Lecture Notes in Computer Science, 1995

Let P be a simple rectilinear polygon with N vertices, endowed with rectilinear metric, and let t... more Let P be a simple rectilinear polygon with N vertices, endowed with rectilinear metric, and let the location of n users in P be given. There are a number of procedures to locate a facility for a given family of users. If a voting procedure is used, the chosen point x should satisfy the following property: no other point y

Research paper thumbnail of Additive Spanners for Circle Graphs and Polygonal Graphs

Lecture Notes in Computer Science, 2008

Research paper thumbnail of Collective Tree 1-Spanners for Interval Graphs

Lecture Notes in Computer Science, 2005

Research paper thumbnail of Line-Distortion, Bandwidth and Path-Length of a Graph

Lecture Notes in Computer Science, 2014

Research paper thumbnail of r-Domination Problems on Homogeneously Ordered Graphs (Extended Abstract)

Research paper thumbnail of A PTAS for the Sparsest Spanners Problem on Apex-Minor-Free Graphs

Lecture Notes in Computer Science, 2008

Research paper thumbnail of Practical Approximation Algorithms for Separable Packing Linear Programs

Lecture Notes in Computer Science, 2001

Research paper thumbnail of New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs

Lecture Notes in Computer Science, 2010

ABSTRACT A distance-k matching in a graph G is matching M in which the distance between any two e... more ABSTRACT A distance-k matching in a graph G is matching M in which the distance between any two edges of M is at least k. A distance-2 matching is more commonly referred to as an induced matching. In this paper, we show that when G is weakly chordal, the size of the largest induced matching in G is equal to the minimum number of co-chordal subgraphs of G needed to cover the edges of G, and that the co-chordal subgraphs of a minimum cover can be found in polynomial time. Using similar techniques, we show that the distance-k matching problem for k > 1 is tractable for weakly chordal graphs when k is even, and is NP-hard when k is odd. For dually chordal graphs, we use properties of hypergraphs to show that the distance-k matching problem is solvable in polynomial time whenever k is odd, and NP-hard when k is even. Motivated by our use of hypergraphs, we define a class of hypergraphs which lies strictly in between the well studied classes of acyclic hypergraphs and normal hypergraphs.

Research paper thumbnail of Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Studies in Computational Intelligence, 2015

Research paper thumbnail of On the Minimum Eccentricity Shortest Path Problem

Lecture Notes in Computer Science, 2015

Research paper thumbnail of Diameters, centers, and approximating trees of delta-hyperbolicgeodesic spaces and graphs

Proceedings of the Twenty Fourth Annual Symposium on Computational Geometry, Jun 9, 2008

Research paper thumbnail of Discrete Applied Mathematics 98 (2000) 191--207

ABSTRACT For an undirected graph G the kth power G of G is the graph with the same vertex set as ... more ABSTRACT For an undirected graph G the kth power G of G is the graph with the same vertex set as G where two vertices are adjacent i# their distance is at most k in G. In this paper we prove that every LexBFS-ordering of a distance-hereditary graph is both a common perfect elimination ordering of all even powers and a common semi-simplicial ordering of all powers of this graph. 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. 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. ? 2000 Elsevier Science B.V. All rights reserved.

Research paper thumbnail of Provably Good Global Buffering by Generalized

Research paper thumbnail of Generalized Powers of Graphs and Their Algorithmic Use

Lecture Notes in Computer Science, 2006

Research paper thumbnail of The Algorithmic Use of Hypertree Structure and Maximum Neighbourhood Orderings

Proceedings of the 20th International Workshop on Graph Theoretic Concepts in Computer Science, Jun 16, 1994

Research paper thumbnail of Navigating in a Graph by Aid of Its Spanning Tree Metric

Siam Journal on Discrete Mathematics, 2011

Research paper thumbnail of Homogeneously orderable graphs and the Steiner tree problem

Lecture Notes in Computer Science, 1995

ABSTRACT In this paper we introduce homogeneously orderable graphs which are a common generalizat... more ABSTRACT In this paper we introduce homogeneously orderable graphs which are a common generalization of distance-hereditary graphs, dually chordal graphs and homogeneous graphs. We present a characterization of the new class in terms of a tree structure of the closed neighbourhoods of homogeneous sets in 2-graphs which is closely related to the defining elimination ordering.

Research paper thumbnail of LexBFS-orderings and powers of graphs

Lecture Notes in Computer Science, 1997

For an undirected graph G the k-th power G k of G is the graph with the same vertex set as G wher... more For an undirected graph G the k-th power G k of G is the graph with the same vertex set as G where two vertices are adjacent iff their distance is at most k in G. In this paper we consider LexBFS-orderings of chordal, distance-hereditaxy and HHD-free graphs (the graphs where each cycle of length at least five has two chords) with respect to their powers. We show that any LexBFS-ordering of a chordal graph is a common perfect elimination ordering of all odd powers of this graph, and any LexBFS-ordering of a distance-hereditary graph is a common perfect elimination ordering of all its even powers. It is wellknown that any LexBFS-ordering of a HHD-free graph is a so-called semi-simplicial ordering. We show, that any LexBFS-ordering of a HHD-free graph is a common semi-simplicial ordering of all its odd powers. Moreover we characterize those chordal, distance-hereditary and HHD-free graphs by forbidden isometric subgraphs for which any LexBFS-ordering of the graph is a common perfect elimination ordering of all its nontrivial powers. 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.

Research paper thumbnail of Effective network monitoring

Proceedings. 13th International Conference on Computer Communications and Networks (IEEE Cat. No.04EX969), 2004

Research paper thumbnail of A linear-time algorithm for finding a central vertex of a chordal graph

Lecture Notes in Computer Science, 1994

Research paper thumbnail of On condorcet and median points of simple rectilinear polygons

Lecture Notes in Computer Science, 1995

Let P be a simple rectilinear polygon with N vertices, endowed with rectilinear metric, and let t... more Let P be a simple rectilinear polygon with N vertices, endowed with rectilinear metric, and let the location of n users in P be given. There are a number of procedures to locate a facility for a given family of users. If a voting procedure is used, the chosen point x should satisfy the following property: no other point y

Research paper thumbnail of Additive Spanners for Circle Graphs and Polygonal Graphs

Lecture Notes in Computer Science, 2008

Research paper thumbnail of Collective Tree 1-Spanners for Interval Graphs

Lecture Notes in Computer Science, 2005

Research paper thumbnail of Line-Distortion, Bandwidth and Path-Length of a Graph

Lecture Notes in Computer Science, 2014

Research paper thumbnail of r-Domination Problems on Homogeneously Ordered Graphs (Extended Abstract)

Research paper thumbnail of A PTAS for the Sparsest Spanners Problem on Apex-Minor-Free Graphs

Lecture Notes in Computer Science, 2008

Research paper thumbnail of Practical Approximation Algorithms for Separable Packing Linear Programs

Lecture Notes in Computer Science, 2001

Research paper thumbnail of New Min-Max Theorems for Weakly Chordal and Dually Chordal Graphs

Lecture Notes in Computer Science, 2010

ABSTRACT A distance-k matching in a graph G is matching M in which the distance between any two e... more ABSTRACT A distance-k matching in a graph G is matching M in which the distance between any two edges of M is at least k. A distance-2 matching is more commonly referred to as an induced matching. In this paper, we show that when G is weakly chordal, the size of the largest induced matching in G is equal to the minimum number of co-chordal subgraphs of G needed to cover the edges of G, and that the co-chordal subgraphs of a minimum cover can be found in polynomial time. Using similar techniques, we show that the distance-k matching problem for k > 1 is tractable for weakly chordal graphs when k is even, and is NP-hard when k is odd. For dually chordal graphs, we use properties of hypergraphs to show that the distance-k matching problem is solvable in polynomial time whenever k is odd, and NP-hard when k is even. Motivated by our use of hypergraphs, we define a class of hypergraphs which lies strictly in between the well studied classes of acyclic hypergraphs and normal hypergraphs.

Research paper thumbnail of Core-Periphery Models for Graphs Based on their δ-Hyperbolicity: An Example Using Biological Networks

Studies in Computational Intelligence, 2015