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Jungles, bundles, and fixed parameter tractabilityDec 07 2011Aug 02 2012We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion problems are FPT ... More

Long Circuits and Large Euler SubgraphsApr 21 2013An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in ... More

A subexponential parameterized algorithm for Proper Interval CompletionFeb 13 2014In the Proper Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into a proper interval graph, i.e., a graph admitting an intersection model of equal-length intervals on a line. ... More

Rank-width and Tree-width of H-minor-free GraphsOct 01 2009We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph ... More

Bidimensionality and KernelsJun 17 2016Feb 05 2019Bidimensionality Theory was introduced by [E.D. Demaine, F.V. Fomin, M.Hajiaghayi, and D.M. Thilikos. Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs, J. ACM, 52 (2005), pp.866--893] as a tool to obtain sub-exponential ... More

On the Parameterized Complexity of Graph Modification to First-Order Logic PropertiesMay 11 2018Feb 26 2019We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number of sufficient ... More

Spanning Circuits in Regular MatroidsJul 19 2016We consider the fundamental Matroid Theory problem of finding a circuit in a matroid spanning a set T of given terminal elements. For graphic matroids this corresponds to the problem of finding a simple cycle passing through a set of given terminal edges ... More

Covering vectors by spaces: Regular matroidsOct 06 2017Seymour's decomposition theorem for regular matroids is a fundamental result with a number of combinatorial and algorithmic applications. In this work we demonstrate how this theorem can be used in the design of parameterized algorithms on regular matroids. ... More

Structured Connectivity AugmentationJun 13 2017We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition of G and H ... More

Algorithms parameterized by vertex cover and modular width, through potential maximal cliquesApr 15 2014In this paper we give upper bounds on the number of minimal separators and potential maximal cliques of graphs w.r.t. two graph parameters, namely vertex cover ($\operatorname{vc}$) and modular width ($\operatorname{mw}$). We prove that for any graph, ... More

Knot Diagrams of Treewidth TwoApr 05 2019Apr 08 2019In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram ... More

Parameterized k-Clustering: The distance matters!Feb 22 2019We consider the $k$-Clustering problem, which is for a given multiset of $n$ vectors $X\subset \mathbb{Z}^d$ and a nonnegative number $D$, to decide whether $X$ can be partitioned into $k$ clusters $C_1, \dots, C_k$ such that the cost \[\sum_{i=1}^k \min_{c_i\in ... More

Exploring Subexponential Parameterized Complexity of Completion ProblemsSep 16 2013May 13 2014Let ${\cal F}$ be a family of graphs. In the ${\cal F}$-Completion problem, we are given a graph $G$ and an integer $k$ as input, and asked whether at most $k$ edges can be added to $G$ so that the resulting graph does not contain a graph from ${\cal ... More

Kernels for (connected) Dominating Set on graphs with Excluded Topological subgraphsSep 30 2012Oct 25 2017We give the first linear kernels for the (Connected) Dominating Set problems on H-topological minor free graphs. We prove the existence of polynomial time algorithms that, for a given H-topological-minor-free graph G and a positive integer k, output an ... More

Low-rank binary matrix approximation in column-sum normApr 12 2019We consider $\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\times n$ matrix ${\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\bf A} -{\bf B}||_1$. We show ... More

Covering Vectors by Spaces in Perturbed Graphic Matroids and Their DualsFeb 19 2019Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P, where I is the ... More

Going Far From DegeneracyFeb 07 2019Feb 14 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More

Approximation Schemes for Low-Rank Binary Matrix Approximation ProblemsJul 18 2018We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it, we obtain the ... More

Partial complementation of graphsApr 29 2018A partial complement of the graph $G$ is a graph obtained from $G$ by complementing all the edges in one of its induced subgraphs. We study the following algorithmic question: for a given graph $G$ and graph class $\mathcal{G}$, is there a partial complement ... More

Subexponential fixed-parameter tractability of cluster editingDec 19 2011Jan 30 2013In the Correlation Clustering, also known as Cluster Editing, we are given an undirected n-vertex graph G and a positive integer k. The task is to decide if G can be transformed into a cluster graph, i.e., a disjoint union of cliques, by changing at most ... More

Beyond Bidimensionality: Parameterized Subexponential Algorithms on Directed GraphsJan 06 2010We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf Out-Branching}, which is ... More

Reducing Topological Minor Containment to the Unique Linkage TheoremApr 05 2019In the Topological Minor Containment problem (TMC) problem two undirected graphs, $G$ and $H$ are given and the objective is to check whether $G$ contains $H$ as a topological minor. Grohe, Kawarabayashi, Marx, and Wollan~[STOC 2011] resolved the parameterized ... More

Conserving controversies of melting line of graphite and grapheneJan 23 2019Investigation of melting line of graphite and liquid carbon has long history. However, up to now there are still numerous controversies in the field, for instance, the melting temperatures obtained in different experiments are in very bad agrement. In ... More

Subexponential Parameterized Algorithm for Minimum Fill-inApr 12 2011The Minimum Fill-in problem is to decide if a graph can be triangulated by adding at most k edges. Kaplan, Shamir, and Tarjan [FOCS 1994] have shown that the problem is solvable in time O(2^(O(k)) + k2 * nm) on graphs with n vertices and m edges and thus ... More

Finding Induced Subgraphs via Minimal TriangulationsSep 29 2009Dec 22 2009Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulations problems including Minimum Fill-in and Treewidth. We discover unexpected applications of these notions ... More

Treewidth computation and extremal combinatoricsMar 09 2008May 05 2008For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices ... More

Subexponential parameterized algorithm for computing the cutwidth of a semi-complete digraphJan 30 2013Cutwidth of a digraph is a width measure introduced by Chudnovsky, Fradkin, and Seymour [4] in connection with development of a structural theory for tournaments, or more generally, for semi-complete digraphs. In this paper we provide an algorithm with ... More

Bidimensionality and Geometric GraphsJul 12 2011Nov 07 2011In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric ... More

Vertex Cover Structural Parameterization RevisitedMar 02 2016A pseudoforest is a graph whose connected components have at most one cycle. Let X be a pseudoforest modulator of graph G, i. e. a vertex subset of G such that G-X is a pseudoforest. We show that Vertex Cover admits a polynomial kernel being parameterized ... More

A Polynomial kernel for Proper Interval Vertex DeletionApr 22 2012It is known that the problem of deleting at most k vertices to obtain a proper interval graph (Proper Interval Vertex Deletion) is fixed parameter tractable. However, whether the problem admits a polynomial kernel or not was open. Here, we answers this ... More

Parameterized Algorithms for Partial Cover ProblemsFeb 12 2008Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with as ... More

Inclusive electron scattering from nuclei in the quasielastic region at large momentum transferDec 10 2008Experiment E02-019, performed in Hall C at the Thomas Jefferson National Accelerator Facility (TJNAF), was a measurement of inclusive electron cross sections for several nuclei ($^{2}$H,$^{3}$He, $^{4}$He, $^{9}$Be,$^{12}$C, $^{63}$Cu, and $^{197}$Au) ... More

Anomalous behavior of dispersion of longitudinal and transverse collective excitations in waterApr 04 2019We study the dependence of the excitation frequency of water along an isochore and an isotherm crossing the region of density anomaly. We have shown that the frequency of the longitudinal excitations demonstrated anomalous dependence on temperature along ... More

Largest chordal and interval subgraphs faster than 2^nNov 16 2013We prove that in an n-vertex graph, induced chordal and interval subgraphs with the maximum number of vertices can be found in time $O(2^{\lambda n})$ for some $\lambda<1$. These are the first algorithms breaking the trivial $2^n n^{O(1)}$ bound of the ... More

Minimizing Rosenthal Potential in Multicast GamesSep 26 2013A multicast game is a network design game modelling how selfish non-cooperative agents build and maintain one-to-many network communication. There is a special source node and a collection of agents located at corresponding terminals. Each agent is interested ... More

Using Combinatorics to Prune Search Trees: Independent and Dominating SetDec 05 2006Dec 14 2006This paper has been withdrawn by the author.

Inclusive inelastic electron scattering from nucleiAug 19 2008Inclusive electron scattering from nuclei at large x and $Q^2$ is the result of a reaction mechanism that includes both quasi--elastic scattering from nucleons and deep inelastic scattering from the quark constituents of the nucleons. Data in this regime ... More

New analysis of the common nuclear dependence of the EMC effect and short-range correlationsSep 07 2012The strong repulsive core of the nucleon-nucleon (NN) interaction at short distances prevents nucleons from becoming close to each other. This gives rise to high-momentum nucleons in the nucleus that cannot be explained in the context of the mean field ... More

First results from the NPDGamma experiment at the Spallation Neutron SourceSep 07 2012The NPDGamma experiment aims to measure the parity-odd correlation between the neutron spin and the direction of the emitted photon in neutron-proton capture. A parity violating asymmetry (to be measured to 10$^{-8}$) from this process can be directly ... More

Moser Polynomials and Eulerian NumbersMar 10 2019Article presents a short investigation into some properties of the Moser polynomials which appear in various problems from algebraic combinatorics. For instance, these polynomials can be used to solve the Generalized Moser's Problem on multiset recovery: ... More

Bidimensionality and EPTASMay 29 2010Nov 03 2011Bidimensionality theory is a powerful framework for the development of metaalgorithmic techniques. It was introduced by Demaine et al. as a tool to obtain sub-exponential time parameterized algorithms for problems on H-minor free graphs. Demaine and Hajiaghayi ... More

On Integer Programming and the Path-width of the Constraint MatrixJul 18 2016Nov 03 2016In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP) is an important ... More

Representative Sets of Product FamiliesFeb 17 2014A subfamily ${\cal F}'$ of a set family ${\cal F}$ is said to $q$-{\em represent} ${\cal F}$ if for every $A \in {\cal F}$ and $B$ of size $q$ such that $A \cap B = \emptyset$ there exists a set $A' \in {\cal F}'$ such that $A' \cap B = \emptyset$. In ... More

Computing Tree-depth Faster Than $2^{n}$Jun 17 2013A connected graph has tree-depth at most $k$ if it is a subgraph of the closure of a rooted tree whose height is at most $k$. We give an algorithm which for a given $n$-vertex graph $G$, in time $\mathcal{O}(1.9602^n)$ computes the tree-depth of $G$. ... More

A subexponential parameterized algorithm for Interval CompletionFeb 13 2014Nov 10 2014In the Interval Completion problem we are given a graph G and an integer k, and the task is to turn G using at most k edge additions into an interval graph, i.e., a graph admitting an intersection model of intervals on a line. Motivated by applications ... More

On the parameterized complexity of cutting a few vertices from a graphApr 23 2013Oct 01 2013We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le t$. We show that ... More

Parameterized Complexity of the Anchored k-Core Problem for Directed GraphsApr 22 2013Sep 17 2013Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such that all but ... More

Fine-grained complexity of integer programming: The case of bounded branch-width and rankJul 18 2016We use the Exponential Time and Strong Exponential Time hypotheses (ETH & SETH) to provide conditional lower bounds on the solvability of the integer programming (IP) problem. We provide evidence that the running times of known pseudo-polynomial time ... More

Exact Algorithms via Monotone Local SearchDec 05 2015We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the family contains ... More

Kernels for (connected) Dominating Set on graphs with Excluded Topological subgraphsSep 30 2012Nov 14 2014We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor. In other words, we give polynomial time algorithms that, for a given H-topological-minor-free graph G ... More

Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help?Jun 21 2012Sep 26 2013We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations ... More

On the tractability of optimization problems on H-graphsSep 27 2017Apr 25 2018For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class was introduced ... More

The superpotential method for chiral cosmological models connected with the modified gravityApr 25 2019We consider the Chiral Cosmological Models (CCM) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed and the method of construction of CCM admitting ... More

Upper Bounds For Hitting Times Of Random Walks On Sparse GraphsFeb 13 2017We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random walk on a connected ... More

Approximating acyclicity parameters of sparse hypergraphsSep 22 2008The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx, who introduced the fractional ... More

Bidimensionality and KernelsJun 17 2016Bidimensionality theory was introduced by Demaine et al. in 2005 as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. Demaine and Hajiaghayi extended the theory to obtain polynomial time approximation schemes (PTASs) ... More

Finding Detours is Fixed-parameter TractableJul 26 2016May 03 2017We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than ... More

A Linear Vertex Kernel for Maximum Internal Spanning TreeJul 20 2009Mar 03 2012We present a polynomial time algorithm that for any graph G and integer k >= 0, either finds a spanning tree with at least k internal vertices, or outputs a new graph G' on at most 3k vertices and an integer k' such that G has a spanning tree with at ... More

Finding Detours is Fixed-parameter TractableJul 26 2016We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than ... More

Tight Bounds for Subgraph Isomorphism and Graph HomomorphismJul 14 2015We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph $G$ to graph $H$ cannot be done in time $|V(H)|^{o(|V(G)|)}$. Combined with the reduction of Cygan, Pachocki, and Soca{\l}a, our result rules ... More

Lower Bounds for the Graph Homomorphism ProblemFeb 19 2015The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring ... More

On the Parameterized Complexity of Graph Modification to First-Order Logic PropertiesMay 11 2018Oct 30 2018We consider the problems of deciding whether an input graph can be modified by removing/adding at most k vertices/edges such that the result of the modification satisfies some property definable in first-order logic. We establish a number of sufficient ... More

Parameterized Complexity of Firefighting RevisitedSep 22 2011The Firefighter problem is to place firefighters on the vertices of a graph to prevent a fire with known starting point from lighting up the entire graph. In each time step, a firefighter may be permanently placed on an unburned vertex and the fire spreads ... More

Knot Diagrams of Treewidth TwoApr 05 2019In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram ... More

Efficient Computation of Representative Sets with Applications in Parameterized and Exact AlgorithmsApr 16 2013Feb 22 2016We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact exponential time algorithms. The applications of our approach ... More

Parameterized Low-Rank Binary Matrix ApproximationMar 16 2018We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an integer r, the "simplicity" ... More

Preventing Unraveling in Social Networks Gets HarderApr 23 2013The behavior of users in social networks is often observed to be affected by the actions of their friends. Bhawalkar et al. \cite{bhawalkar-icalp} introduced a formal mathematical model for user engagement in social networks where each individual derives ... More

Loop-erased walks and total positivityApr 12 2000We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights with nonnegative ... More

On Elementary Theories of GLP-AlgebrasDec 15 2014There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the varieties of modal ... More

Repeated games of incomplete information with large sets of statesMay 30 2012Dec 25 2013The famous theorem of R.Aumann and M.Maschler states that the sequence of values of an N-stage zero-sum game G_N with incomplete information on one side converges as N tends to infinity, and the error term is bounded by a constant divided by square root ... More

How to Hunt an Invisible Rabbit on a GraphFeb 19 2015Feb 20 2015We investigate Hunters & Rabbit game, where a set of hunters tries to catch an invisible rabbit that slides along the edges of a graph. We show that the minimum number of hunters required to win on an (n\times m)-grid is \lfloor min{n,m}/2\rfloor+1. We ... More

Faster Algorithms for Finding and Counting SubgraphsDec 11 2009In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$ vertices respectively ... More

Dune-CurvilinearGrid: Parallel Dune Grid Manager for Unstructured Tetrahedral Curvilinear MeshesDec 09 2016We introduce the dune-curvilineargrid module. The module provides the self-contained, parallel grid manager, as well as the underlying elementary curvilinear geometry module dune-curvilineargeometry. This work is motivated by the need for reliable and ... More

Searching for flavor dependence in nuclear quark behaviorMar 29 2019The observed correlation between the EMC effect and the contribution of short-range correlations (SRCs) in nuclei suggests that the modification of the quark distributions of bound protons and neutrons might occur within SRCs. This raises the possibility ... More

Cluster algebras and triangulated surfaces. Part II: Lambda lengthsOct 20 2012Aug 13 2018For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric side, this requires ... More

Plato's cave and differential formsDec 31 2017Apr 21 2019In the 1970s and again in the 1990s, Gromov gave a number of theorems and conjectures motivated by the notion that the real homotopy theory of compact manifolds and simplicial complexes influences the geometry of maps between them. The main technical ... More

Kernels for Feedback Arc Set In TournamentsJul 13 2009Oct 29 2009A tournament T=(V,A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs ... More

Noncommutative Schur functions, switchboards, and Schur positivityOct 02 2015Jul 10 2016The machinery of noncommutative Schur functions provides a general tool for obtaining Schur expansions for combinatorially defined symmetric functions. We extend this approach to a wider class of symmetric functions, explore its strengths and limitations, ... More

Kernel(s) for Problems With no Kernel: On Out-Trees With Many LeavesOct 27 2008Nov 06 2008The {\sc $k$-Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) with at least $k$ leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms {alonLNCS4596,AlonFGKS07fsttcs,BoDo2,KnLaRo}. ... More

Fully polynomial-time parameterized computations for graphs and matrices of low treewidthNov 04 2015We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero entries. In ... More

Parameterized Complexity of Superstring ProblemsFeb 05 2015In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as substrings. We obtain ... More

Metric Dimension of Bounded Tree-length GraphsFeb 08 2016The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and y there is ... More

Parameterized Complexity of Secluded Connectivity ProblemsFeb 13 2015Apr 21 2015The Secluded Path problem models a situation where a sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure, which is the total weight of vertices in ... More

Algorithm for Finding $k$-Vertex Out-trees and its Application to $k$-Internal Out-branching ProblemMar 05 2009An out-tree $T$ is an oriented tree with only one vertex of in-degree zero. A vertex $x$ of $T$ is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree ... More

Going Far From DegeneracyFeb 07 2019An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least d+1. The proof of Erd\H{o}s and ... More

(Meta) KernelizationApr 04 2009Sep 25 2013In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this ... More

Tight Lower Bounds on Graph Embedding ProblemsFeb 16 2016We prove that unless the Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph $G$ to graph $H$ cannot be done in time $|V(H)|^{o(|V(G)|)}$. We also show an exponential-time reduction from Graph Homomorphism to Subgraph ... More

Hitting forbidden minors: Approximation and KernelizationOct 07 2010We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any graph from the ... More

Better Algorithms and Bounds for Directed Maximum Leaf ProblemsJul 07 2007The {\sc Directed Maximum Leaf Out-Branching} problem is to find an out-branching (i.e. a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we improve known parameterized algorithms and combinatorial bounds ... More

Decomposition of Map Graphs with ApplicationsMar 04 2019Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and Thomas that states ... More

A O(c^k n) 5-Approximation Algorithm for TreewidthApr 23 2013We give an algorithm that for an input n-vertex graph G and integer k>0, in time 2^[O(k)]n either outputs that the treewidth of G is larger than k, or gives a tree decomposition of G of width at most 5k+4. This is the first algorithm providing a constant ... More

Subexponential parameterized algorithms for planar and apex-minor-free graphs via low treewidth pattern coveringApr 20 2016We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth $\mathcal{O}(\sqrt{k}\log ... More

Large induced subgraphs via triangulations and CMSOSep 06 2013We obtain an algorithmic meta-theorem for the following optimization problem. Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an integer. For a given graph G, the task is to maximize |X| subject to the following: there is a ... More

k-Gap Interval GraphsDec 14 2011Dec 16 2011We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an interval associated ... More

On a question of Krajewski'sDec 05 2017In this paper we provide a (negative) solution to a problem posed by Stanis{\l}aw Krajewski. Consider a recursively enumerable theory U and a finite expansion of the signature of U that contains at least one predicate symbol of arity $\ge$ 2. We show ... More

A surface containing a line and a circle through each point is a quadricOct 11 2011Aug 15 2012We prove that a surface in real 3-space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.

Measurable operators and the asymptotics of heat kernels and zeta functionsJan 17 2012In this note we answer some questions inspired by the introduction, by Alain Connes, of the notion of measurable operators using Dixmier traces. These questions concern the relationship of measurability to the asymptotics of $\zeta-$functions and heat ... More

On the interpolation of integer-valued polynomialsAug 16 2011It is well known, that if polynomial with rational coefficients of degree $n$ takes integer values in points $0,1,...,n$ then it takes integer values in all integer points. Are there sets of $n+1$ points with the same property in other integral domains? ... More

On stable conjugacy of finite subgroups of the plane Cremona group, IJun 13 2013Jul 02 2013We discuss the problem of stable conjugacy of finite subgroups of Cremona groups. We show that the group $H^1(G,Pic(X))$ is a stable birational invariant and compute this group in some cases.

On knot groups acting on treesJul 17 2018A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag--Solitar group ($GBS$ group). We prove that a 1-knot group $G$ is $GBS$ group iff $G$ is a torus-knot group and describe ... More