Yury Orlovich - Profile on Academia.edu (original) (raw)

Papers by Yury Orlovich

Research paper thumbnail of Scale-free spanning trees: complexity, bounds and algorithms

arXiv (Cornell University), May 27, 2020

We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a... more We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scalefree spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the s-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data.

Research paper thumbnail of On some optimization problems for star-free graphs

arXiv (Cornell University), Jun 25, 2001

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Research paper thumbnail of Scale-free spanning trees: complexity, bounds and algorithms

arXiv (Cornell University), May 27, 2020

We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a... more We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scalefree spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the s-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data.

Research paper thumbnail of Scale-Free Spanning Trees and Their Application in Genomic Epidemiology

Journal of Computational Biology, 2021

We study the algorithmic problem of finding the most ''scale-free-like'' spanning tree of a conne... more We study the algorithmic problem of finding the most ''scale-free-like'' spanning tree of a connected graph. This problem is motivated by the fundamental problem of genomic epidemiology: given viral genomes sampled from infected individuals, reconstruct the transmission network (''who infected whom''). We use two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF (-scale free) and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic and bipartite graphs. We propose two integer linear programming (ILP) formulations for the s-SF Spanning Tree problem, and experimentally assess its performance using simulated and experimental data. In particular, we demonstrate that the ILP-based approach allows for accurate reconstruction of transmission histories of several hepatitis C outbreaks.

Research paper thumbnail of On a Special Case of the Generalized Neighbourhood Problem

For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more For a given finite class of finite graphs H, a graph G is called a realization of H if the neighbourhood of its any vertex induces the subgraph isomorphic to a graph of H. We consider the following problem known as the Generalized Neighbourhood Problem (GNP): given a finite class of finite graphs H, does there exist a non-empty graph G that is a realization of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices. Comment: 13 pages, 3 figures, in Russian

Research paper thumbnail of On some optimization problems for star-free graphs

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Research paper thumbnail of Squares of Intersection Graphs and Induced Matchings

Electronic Notes in Discrete Mathematics, 2006

We consider the squares of intersection graphs of hypergraphs and simple graphs. The Berge-type c... more We consider the squares of intersection graphs of hypergraphs and simple graphs. The Berge-type characterization for squares of intersection graphs of hypergraphs is obtained. The analogue of Whitney theorem for squares of intersection graphs of trees is proved. Using the connection between induced matchings of graph and independent sets of square of line graph, new polynomial solvable cases for the weighted induced matching problem are obtained.

Research paper thumbnail of On Hamilton Cycles in Locally Connected Graphs with Vertex Degree Constraints

Electronic Notes in Discrete Mathematics, 2007

It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G) = 5... more It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G) = 5 and the minimum vertex degree δ(G) ≥ 3 is fully cycle extendable. For Δ(G) ≤ 4, all connected, locally connected graphs, including infinite ones, are explicitly described. The Hamilton Cycle problem for locally connected graphs with Δ(G) ≤ 7 is shown to be NP-complete.

Research paper thumbnail of Scale-free spanning trees: complexity, bounds and algorithms

arXiv (Cornell University), May 27, 2020

We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a... more We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scalefree spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the s-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data.

Research paper thumbnail of On some optimization problems for star-free graphs

arXiv (Cornell University), Jun 25, 2001

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Research paper thumbnail of Scale-free spanning trees: complexity, bounds and algorithms

arXiv (Cornell University), May 27, 2020

We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a... more We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scalefree spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the s-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data.

Research paper thumbnail of Scale-Free Spanning Trees and Their Application in Genomic Epidemiology

Journal of Computational Biology, 2021

We study the algorithmic problem of finding the most ''scale-free-like'' spanning tree of a conne... more We study the algorithmic problem of finding the most ''scale-free-like'' spanning tree of a connected graph. This problem is motivated by the fundamental problem of genomic epidemiology: given viral genomes sampled from infected individuals, reconstruct the transmission network (''who infected whom''). We use two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF (-scale free) and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic and bipartite graphs. We propose two integer linear programming (ILP) formulations for the s-SF Spanning Tree problem, and experimentally assess its performance using simulated and experimental data. In particular, we demonstrate that the ILP-based approach allows for accurate reconstruction of transmission histories of several hepatitis C outbreaks.

Research paper thumbnail of On a Special Case of the Generalized Neighbourhood Problem

For a given finite class of finite graphs H, a graph G is called a realization of H if the neighb... more For a given finite class of finite graphs H, a graph G is called a realization of H if the neighbourhood of its any vertex induces the subgraph isomorphic to a graph of H. We consider the following problem known as the Generalized Neighbourhood Problem (GNP): given a finite class of finite graphs H, does there exist a non-empty graph G that is a realization of H? In fact, there are two modifications of that problem, namely the finite (the existence of a finite realization is required) and infinite one (the realization is required to be infinite). In this paper we show that GNP and its modifications for all finite classes H of finite graphs are reduced to the same problems with an additional restriction on H. Namely, the orders of any two graphs of H are equal and every graph of H has exactly s dominating vertices. Comment: 13 pages, 3 figures, in Russian

Research paper thumbnail of On some optimization problems for star-free graphs

It is shown that in star-free graphs the maximum independent set problem, the minimum dominating ... more It is shown that in star-free graphs the maximum independent set problem, the minimum dominating set problem and the minimum independent dominating set problem are approximable up to constant factor by any maximal independent set.

Research paper thumbnail of Squares of Intersection Graphs and Induced Matchings

Electronic Notes in Discrete Mathematics, 2006

We consider the squares of intersection graphs of hypergraphs and simple graphs. The Berge-type c... more We consider the squares of intersection graphs of hypergraphs and simple graphs. The Berge-type characterization for squares of intersection graphs of hypergraphs is obtained. The analogue of Whitney theorem for squares of intersection graphs of trees is proved. Using the connection between induced matchings of graph and independent sets of square of line graph, new polynomial solvable cases for the weighted induced matching problem are obtained.

Research paper thumbnail of On Hamilton Cycles in Locally Connected Graphs with Vertex Degree Constraints

Electronic Notes in Discrete Mathematics, 2007

It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G) = 5... more It is shown that every connected, locally connected graph with the maximum vertex degree Δ(G) = 5 and the minimum vertex degree δ(G) ≥ 3 is fully cycle extendable. For Δ(G) ≤ 4, all connected, locally connected graphs, including infinite ones, are explicitly described. The Hamilton Cycle problem for locally connected graphs with Δ(G) ≤ 7 is shown to be NP-complete.