The degree prescribed factor problem is to decide if a graph has a subgraph satisfying given degr... more The degree prescribed factor problem is to decide if a graph has a subgraph satisfying given degree prescriptions at each vertex. Lovász, and later Cornuéjols, gave structural descriptions on this problem in case the prescriptions have no two consecutive gaps. We state the Edmonds-Gallai-type structure theorem of Cornuéjols which is only implicit in his paper. In these results the difficulty of checking the property of criticality is near to the original problem. By extending a result of Loebl, we prove that a degree prescription can be reduced to the edge and factor-critical graph packing problem by a ‘gadget’ if and only if all of its gaps have the same parity. With this gadget technique it is possible to obtain a description of the critical components. Finally, we prove two matroidal results. First, the up hulls of the distance vectors of all subgraphs form a contra-polymatroid. Second, we prove that the vertex sets coverable by subgraphs F satisfying the degree prescriptions for...
In this paper we give an analytical description on the structure of solutions to the gas nominati... more In this paper we give an analytical description on the structure of solutions to the gas nomination validation problem in gas transportation networks. These networks are assumed to contain no active devices, only certain hypothetical pipelines, where the flow of gas is modeled by a generalized version of the quadratic Weymouth's equation. The purpose of considering generalized flow formulas is to be able to adapt our results to various gas network optimization problems involving gas flow formulas beyond Weymouth's equation. Such formulas can appear in leaves of branch and bound trees, or they can stem from discretization and linearization carried out at active devices. We call a balanced supply-demand vector a nomination, and the passive nomination validation problem is to decide whether there exist pressures at the nodes generating a given nomination. We prove that in our setup the pressure square vectors generating a given nomination form a one-dimensional connected and co...
In this paper we introduce the upgrading problem for edge-disjoint paths. In the off-line upgradi... more In this paper we introduce the upgrading problem for edge-disjoint paths. In the off-line upgrading problem a supply graph G and two demand graphs H1 and H2 are given on the same vertex set. What is the maximum size of a set F ⊆ E(H1)∩E(H2) such that F has a routing in G which can be extended to a routing of Hi in G, for i = 1, 2? In the online upgrading problem we are given a supply graph G, a demand graph H with a routing and another demand graph H2 such that E(H) ⊆ E(H2). What is the maximum size of a set F ⊆ E(H) such that the restriction of the given routing to F can be extended to routing of H2? Thus, depending on whether the graphs are directed or undirected, we have four different versions. In this paper we give full solution for the case when G is a ring and the demand graphs are stars. All four versions are NP-complete in general.
While Web archive quality is endangered by Web spam, a side effect of the high commercial value o... more While Web archive quality is endangered by Web spam, a side effect of the high commercial value of top-ranked search-engine results, so far Web spam filtering technologies are rarely used by Web archivists. In this paper we make the first attempt to disseminate existing methodology and envision a solution for Web archives to share knowledge and unite efforts in Web spam hunting. We survey the state of the art in Web spam filtering illustrated by the recent Web spam challenge data sets and techniques and describe the filtering solution for archives envisioned in the LiWA—Living Web Archives project.
We use a combination, in the expected order of their strength, of the following classificators: S... more We use a combination, in the expected order of their strength, of the following classificators: SVM over tf.idf, an augmented set of the public statistical spam features, graph stacking and text classification by latent Dirichlet allocation and compression, the latter two only used in our second submission.
Given a bidirected ring with capacities and a demand graph, we present an approximation algorithm... more Given a bidirected ring with capacities and a demand graph, we present an approximation algorithm to the problem of finding the minimum $\alpha$ such that there exists a feasible unsplittable routing of the demands after multiplying each capacity by $\alpha$. We also give an approximation scheme to the problem.
Abstract With continuously increasing capacity utilization of railway networks as well as growing... more Abstract With continuously increasing capacity utilization of railway networks as well as growing requirements on service quality and reliability, railway timetabling is becoming increasingly difficult. Although most timetables are still constructed manually in practice, the demand for advanced automatic timetabling techniques is evident. Long computation times, however, are a major impediment for the use of optimization-based timetabling tools within today's planning process. Focusing on the construction of periodic timetables via the periodic event scheduling problem (PESP), the paper introduces a new decomposition technique to speed up automatic timetabling. The approach is based on solving a sequence of smaller subproblems and can be parameterized to reach a suitable compromise between the two extremes of either simultaneous or sequential planning. Computational results on large timetabling instances for Switzerland's railway network show very promising results. In particular, finding feasible as well as near optimal timetables can be considerably accelerated compared to solving the PESP using the standard MILP formulation.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
The importance of energetic flexibility of distributed energy resources grows with the share of r... more The importance of energetic flexibility of distributed energy resources grows with the share of renewable generation in the power grid. However, the quantitative description and aggregation of flexible resources is challenging. This work proposes the use of zonotopes, a subclass of polytopes, to approximate flexibility. It is shown how optimal zonotopic approximations of flexibility can be computed efficiently for different objectives, and that the aggregation of those sets is tractable with regard to memory and computational complexity for long planning horizons and large populations of systems. In addition, we describe synergistic behavior exhibited by the aggregation of flexibility and illustrate that zonotopes can partly capture these synergy effects.
Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a s... more Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a simple undirected graph is a $k$-matching, so that each of its connected components has at least $j+1$ edges. The maximum non-negative node weighted $j$-restricted $k$-matching problem was recently studied by Li who gave a polynomial-time algorithm and a min-max theorem for $0 \leqslant j < k$, and also proved the NP-hardness of the problem with unit node weights and $2 \leqslant k \leqslant j$. In this paper we derive an Edmonds–Gallai-type decomposition theorem for the $j$-restricted $k$-matching problem with $0 \leqslant j < k$, using the analogous decomposition for $k$-piece packings given by Janata, Loebl and Szabó, and give an alternative proof to the min-max theorem of Li.
ABSTRACT In 1981 András Recski conjectured that, if given a number $q\in \mathbb{N}$, a linearly ... more ABSTRACT In 1981 András Recski conjectured that, if given a number $q\in \mathbb{N}$, a linearly represented matroid $M$, a partition $S_1 \mathbin{\dot{\cup}} \cdots \mathbin{\dot{\cup}} S_n$ of a subset of its ground set $S$ into classes of size $k$, and a prescription $A\subseteq \{0,1,\dots,k\}$ without two consecutive gaps, then one can find in polynomial time an independent set $F$ of $M$ of size $q$ such that $|F \cap S_i|\in A$ for all $1\leq i\leq n$, if one exists. In this paper we prove this conjecture. The proof is based on Lovász&#39; result on the polynomial solvability of the matroid parity problem for linearly represented matroids and on an important technique about jump systems, proved by Sebõ. We give an application to rigidity theory and another one to the unique solvability of linear networks containing memoryless multiports.
... for the notion of a subdivided graph. A similar Gallai Edmonds type theorem for the F-packing... more ... for the notion of a subdivided graph. A similar Gallai Edmonds type theorem for the F-packing problem was proved by Cornu jols and Hartvigsen [2]. We cite this result. Definition 13. (See Cornu jols, Hartvigsen, Pulleyblank [3 ...
... First we show a polynomial time alternating forest algorithm, which is a direct generalizatio... more ... First we show a polynomial time alternating forest algorithm, which is a direct generalization of the classical matching algorithm of Edmonds. ... Our Edmonds type algorithm has the peculiarity that the alternating for-est may cover a vertex twice. ...
In this paper, we introduce the upgrading problem of edge-disjoint paths. In the off-line upgradi... more In this paper, we introduce the upgrading problem of edge-disjoint paths. In the off-line upgrading problem, a supply graph G with integer capacities and two demand graphs H1 and H2 with unit demands are given on the same vertex set. Our task is to determine the maximum size of a set F⊆E(H1)∩E(H2) such that F has an integer routing in
Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new ty... more Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new type of undirected graph packing problem, called the $k$-piece packing problem. A $k$-piece is a simple, connected graph with highest degree exactly $k$ so in the case $k=1$ we get the classical matching problem. They give a polynomial algorithm, a Tutte-type characterization and a Berge-type minimax formula for the $k$-piece packing problem. However, they leave open the question of an Edmonds-Gallai type decomposition. This paper fills this gap by describing such a decomposition. We also prove that the vertex sets coverable by $k$-piece packings have a certain matroidal structure.
The degree prescribed factor problem is to decide if a graph has a subgraph satisfying given degr... more The degree prescribed factor problem is to decide if a graph has a subgraph satisfying given degree prescriptions at each vertex. Lovász, and later Cornuéjols, gave structural descriptions on this problem in case the prescriptions have no two consecutive gaps. We state the Edmonds-Gallai-type structure theorem of Cornuéjols which is only implicit in his paper. In these results the difficulty of checking the property of criticality is near to the original problem. By extending a result of Loebl, we prove that a degree prescription can be reduced to the edge and factor-critical graph packing problem by a ‘gadget’ if and only if all of its gaps have the same parity. With this gadget technique it is possible to obtain a description of the critical components. Finally, we prove two matroidal results. First, the up hulls of the distance vectors of all subgraphs form a contra-polymatroid. Second, we prove that the vertex sets coverable by subgraphs F satisfying the degree prescriptions for...
In this paper we give an analytical description on the structure of solutions to the gas nominati... more In this paper we give an analytical description on the structure of solutions to the gas nomination validation problem in gas transportation networks. These networks are assumed to contain no active devices, only certain hypothetical pipelines, where the flow of gas is modeled by a generalized version of the quadratic Weymouth's equation. The purpose of considering generalized flow formulas is to be able to adapt our results to various gas network optimization problems involving gas flow formulas beyond Weymouth's equation. Such formulas can appear in leaves of branch and bound trees, or they can stem from discretization and linearization carried out at active devices. We call a balanced supply-demand vector a nomination, and the passive nomination validation problem is to decide whether there exist pressures at the nodes generating a given nomination. We prove that in our setup the pressure square vectors generating a given nomination form a one-dimensional connected and co...
In this paper we introduce the upgrading problem for edge-disjoint paths. In the off-line upgradi... more In this paper we introduce the upgrading problem for edge-disjoint paths. In the off-line upgrading problem a supply graph G and two demand graphs H1 and H2 are given on the same vertex set. What is the maximum size of a set F ⊆ E(H1)∩E(H2) such that F has a routing in G which can be extended to a routing of Hi in G, for i = 1, 2? In the online upgrading problem we are given a supply graph G, a demand graph H with a routing and another demand graph H2 such that E(H) ⊆ E(H2). What is the maximum size of a set F ⊆ E(H) such that the restriction of the given routing to F can be extended to routing of H2? Thus, depending on whether the graphs are directed or undirected, we have four different versions. In this paper we give full solution for the case when G is a ring and the demand graphs are stars. All four versions are NP-complete in general.
While Web archive quality is endangered by Web spam, a side effect of the high commercial value o... more While Web archive quality is endangered by Web spam, a side effect of the high commercial value of top-ranked search-engine results, so far Web spam filtering technologies are rarely used by Web archivists. In this paper we make the first attempt to disseminate existing methodology and envision a solution for Web archives to share knowledge and unite efforts in Web spam hunting. We survey the state of the art in Web spam filtering illustrated by the recent Web spam challenge data sets and techniques and describe the filtering solution for archives envisioned in the LiWA—Living Web Archives project.
We use a combination, in the expected order of their strength, of the following classificators: S... more We use a combination, in the expected order of their strength, of the following classificators: SVM over tf.idf, an augmented set of the public statistical spam features, graph stacking and text classification by latent Dirichlet allocation and compression, the latter two only used in our second submission.
Given a bidirected ring with capacities and a demand graph, we present an approximation algorithm... more Given a bidirected ring with capacities and a demand graph, we present an approximation algorithm to the problem of finding the minimum $\alpha$ such that there exists a feasible unsplittable routing of the demands after multiplying each capacity by $\alpha$. We also give an approximation scheme to the problem.
Abstract With continuously increasing capacity utilization of railway networks as well as growing... more Abstract With continuously increasing capacity utilization of railway networks as well as growing requirements on service quality and reliability, railway timetabling is becoming increasingly difficult. Although most timetables are still constructed manually in practice, the demand for advanced automatic timetabling techniques is evident. Long computation times, however, are a major impediment for the use of optimization-based timetabling tools within today's planning process. Focusing on the construction of periodic timetables via the periodic event scheduling problem (PESP), the paper introduces a new decomposition technique to speed up automatic timetabling. The approach is based on solving a sequence of smaller subproblems and can be parameterized to reach a suitable compromise between the two extremes of either simultaneous or sequential planning. Computational results on large timetabling instances for Switzerland's railway network show very promising results. In particular, finding feasible as well as near optimal timetables can be considerably accelerated compared to solving the PESP using the standard MILP formulation.
2015 54th IEEE Conference on Decision and Control (CDC), 2015
The importance of energetic flexibility of distributed energy resources grows with the share of r... more The importance of energetic flexibility of distributed energy resources grows with the share of renewable generation in the power grid. However, the quantitative description and aggregation of flexible resources is challenging. This work proposes the use of zonotopes, a subclass of polytopes, to approximate flexibility. It is shown how optimal zonotopic approximations of flexibility can be computed efficiently for different objectives, and that the aggregation of those sets is tractable with regard to memory and computational complexity for long planning horizons and large populations of systems. In addition, we describe synergistic behavior exhibited by the aggregation of flexibility and illustrate that zonotopes can partly capture these synergy effects.
Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a s... more Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a simple undirected graph is a $k$-matching, so that each of its connected components has at least $j+1$ edges. The maximum non-negative node weighted $j$-restricted $k$-matching problem was recently studied by Li who gave a polynomial-time algorithm and a min-max theorem for $0 \leqslant j < k$, and also proved the NP-hardness of the problem with unit node weights and $2 \leqslant k \leqslant j$. In this paper we derive an Edmonds–Gallai-type decomposition theorem for the $j$-restricted $k$-matching problem with $0 \leqslant j < k$, using the analogous decomposition for $k$-piece packings given by Janata, Loebl and Szabó, and give an alternative proof to the min-max theorem of Li.
ABSTRACT In 1981 András Recski conjectured that, if given a number $q\in \mathbb{N}$, a linearly ... more ABSTRACT In 1981 András Recski conjectured that, if given a number $q\in \mathbb{N}$, a linearly represented matroid $M$, a partition $S_1 \mathbin{\dot{\cup}} \cdots \mathbin{\dot{\cup}} S_n$ of a subset of its ground set $S$ into classes of size $k$, and a prescription $A\subseteq \{0,1,\dots,k\}$ without two consecutive gaps, then one can find in polynomial time an independent set $F$ of $M$ of size $q$ such that $|F \cap S_i|\in A$ for all $1\leq i\leq n$, if one exists. In this paper we prove this conjecture. The proof is based on Lovász&#39; result on the polynomial solvability of the matroid parity problem for linearly represented matroids and on an important technique about jump systems, proved by Sebõ. We give an application to rigidity theory and another one to the unique solvability of linear networks containing memoryless multiports.
... for the notion of a subdivided graph. A similar Gallai Edmonds type theorem for the F-packing... more ... for the notion of a subdivided graph. A similar Gallai Edmonds type theorem for the F-packing problem was proved by Cornu jols and Hartvigsen [2]. We cite this result. Definition 13. (See Cornu jols, Hartvigsen, Pulleyblank [3 ...
... First we show a polynomial time alternating forest algorithm, which is a direct generalizatio... more ... First we show a polynomial time alternating forest algorithm, which is a direct generalization of the classical matching algorithm of Edmonds. ... Our Edmonds type algorithm has the peculiarity that the alternating for-est may cover a vertex twice. ...
In this paper, we introduce the upgrading problem of edge-disjoint paths. In the off-line upgradi... more In this paper, we introduce the upgrading problem of edge-disjoint paths. In the off-line upgrading problem, a supply graph G with integer capacities and two demand graphs H1 and H2 with unit demands are given on the same vertex set. Our task is to determine the maximum size of a set F⊆E(H1)∩E(H2) such that F has an integer routing in
Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new ty... more Generalizing Kaneko's long path packing problem, Hartvigsen, Hell and Szabó consider a new type of undirected graph packing problem, called the $k$-piece packing problem. A $k$-piece is a simple, connected graph with highest degree exactly $k$ so in the case $k=1$ we get the classical matching problem. They give a polynomial algorithm, a Tutte-type characterization and a Berge-type minimax formula for the $k$-piece packing problem. However, they leave open the question of an Edmonds-Gallai type decomposition. This paper fills this gap by describing such a decomposition. We also prove that the vertex sets coverable by $k$-piece packings have a certain matroidal structure.
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Papers by Jácint Szabó