Jácint Szabó
IBM Research, Business Analytics & Mathematical Sciences, Department Member
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... 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 nomination validation problem in gas transportation networks. These networks are assumed to contain no active devices, only certain hypothetical... 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...
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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 ⊆... 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 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... 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.
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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... 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.
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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... 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.
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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... 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.
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... 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 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... 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.
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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... 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.
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... 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 ...
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... 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... 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. ...
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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... 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
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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... 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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Let $${\mathcal{H}}$$ be a set of undirected graphs. The induced $${\mathcal{H}}$$ -packing problem in an input graph G is to find a subgraph Q of G of maximum size such that each connected component of Q is an induced subgraph of G and... more
Let $${\mathcal{H}}$$ be a set of undirected graphs. The induced $${\mathcal{H}}$$ -packing problem in an input graph G is to find a subgraph Q of G of maximum size such that each connected component of Q is an induced subgraph of G and is isomorphic to some member of $${\mathcal{H}}$$ . In this paper we focus on the case when $${\mathcal{H}}$$ consists of factor-critical graphs and a certain family of ‘propellers’. Clarifying the methods developed in the related theory of non-induced graph packings, we show a Gallai–Edmonds type structure theorem and a Berge–Tutte type minimax formula. We also give an Edmonds type alternating forest algorithm for the case when $${\mathcal{H}}$$ consists of a sequential set of stars and factor-critical graphs. This simplifies the related result of Egawa, Kano and Kelmans.
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Given a graph G and a stable set S. Assume that the edge set of G can be partitioned into two spanning trees. We raise the question, whether it can be partitioned into spanning trees F 1 and F 2 in such a way that at every vertex the... more
Given a graph G and a stable set S. Assume that the edge set of G can be partitioned into two spanning trees. We raise the question, whether it can be partitioned into spanning trees F 1 and F 2 in such a way that at every vertex the degrees in F 1 and in F 2 differ at most 1. We show that if |S|≤3 then such a partition indeed exists, while otherwise it is not necessarily so.
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In this paper we first prove that if the edge set of an undirected graph is the disjoint union of two of its spanning trees, then for every subset P of edges there exists a spanning tree decomposition that cuts P into two (almost) equal... more
In this paper we first prove that if the edge set of an undirected graph is the disjoint union of two of its spanning trees, then for every subset P of edges there exists a spanning tree decomposition that cuts P into two (almost) equal parts. The main result of the paper is a further extension of this claim: If the edge set of a graph is the disjoint union of two of its spanning trees, then for every stable set of vertices of size 3, there exists such a spanning tree decomposition that cuts the stars of these vertices into (almost) equal parts. This result fails for 4 instead of 3. The proofs are elementary.
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... For each edge e /∈ Pi which is incident to si ∈ S do the following, see Fig. 7. Subdivide e by a new vertex ei and double the edge siei. Add these two parallel siei-edges to Pi resulting in the new subpartition P . Note that P... more
... For each edge e /∈ Pi which is incident to si ∈ S do the following, see Fig. 7. Subdivide e by a new vertex ei and double the edge siei. Add these two parallel siei-edges to Pi resulting in the new subpartition P . Note that P consists of stars of pairwise non-adjacent vertices. ...
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LetT1,T2, ...,Ttbe disjoint?-element sets and let their union be denoted byS. LetAbe a subset of 0, 1, 2, ...,?. For an integer 0 ?c?t, a subsetX?Sis called (?c)-legalif |X?Ti| ?Aholds for at leastcsubscripts and it is calledc-legalif... more
LetT1,T2, ...,Ttbe disjoint?-element sets and let their union be denoted byS. LetAbe a subset of 0, 1, 2, ...,?. For an integer 0 ?c?t, a subsetX?Sis called (?c)-legalif |X?Ti| ?Aholds for at leastcsubscripts and it is calledc-legalif |X?Ti| ?Aholds for exactlycsubscripts. LetMbe a matroid onS. In this paper we study problems like ?Does there exist a (?c)-legal (orc-legal) independent set of given cardinality inM?? Observe that ifA= {0,?} andc=tthen both problems reduce to the matroid?-parity problem (in particular, to the classical matroid parity problem for?= 2). The problems have some motivations from engineering applications and are also related to the more recent theory of jump systems.
In this paper we demonstrate the applicability of latent Dirichlet allocation (LDA) for classifying large Web document collections. One of our main results is a novel influence model that gives a fully generative model of the document... more
In this paper we demonstrate the applicability of latent Dirichlet allocation (LDA) for classifying large Web document collections. One of our main results is a novel influence model that gives a fully generative model of the document content taking linkage into account. In our setup, topics propagate along links in such a way that linked documents directly influence the words in the linking document. As another main contribution we develop LDA specific boosting of Gibbs samplers resulting in a significant speedup in our experiments. The inferred LDA model can be applied for classification as dimensionality reduction similarly to latent semantic indexing. In addition, the model yields link weights that can be applied in algorithms to process the Web graph; as an example we deploy LDA link weights in stacked graphical learning. By using Weka's BayesNet classifier, in terms of the AUC of classification, we achieve 4% improvement over plain LDA with BayesNet and 18% over tf.idf wit...
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... For components of Z having no blade in them use the previous paragraph to construct an H-factor. For the remaining part construct a maximum matching by Edmonds&amp;amp;#x27; algorithm. ... Theorem 2.6 is specialized to the... more
... For components of Z having no blade in them use the previous paragraph to construct an H-factor. For the remaining part construct a maximum matching by Edmonds&amp;amp;#x27; algorithm. ... Theorem 2.6 is specialized to the following theorem of Cornuéjols, Hartvigsen and Pulleyblank [1]. ...
ABSTRACT We are concerned with routing problems arising in special kinds of SDH networks, called daisy networks. Beside the capacity constraints, some disjoint edge-sets of the network, called arcs, are also prescribed. Our goal is to... more
ABSTRACT We are concerned with routing problems arising in special kinds of SDH networks, called daisy networks. Beside the capacity constraints, some disjoint edge-sets of the network, called arcs, are also prescribed. Our goal is to find a routing of the demands satisfying the capacities with the additional constraint that whenever a path (with value 1) enters an arc then it uses capacity 1 on all edges of that arc. We consider two types of arc-systems and give algorithms and computational results of integer programming formulations. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(2), 116–121 2006These authors are members of the Egerváry Research Group (EGRES) of the Hungarian Academy of Sciences