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- research-articleJuly 2024
Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph Classes
LICS '24: Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer ScienceJuly 2024, Article No.: 68, Pages 1–12https://doi.org/10.1145/3661814.3662089Disjoint-paths logic, denoted FO+ DP, extends first-order logic (FO) with atomic predicates dpk[(x1, y1), …, (xk, yk)], expressing the existence of internally vertex-disjoint paths between xi and yi, for 1 ≤ i ≤ k. We prove that for every graph class ...
- research-articleMay 2024
Budget-feasible Egalitarian Allocation of Conflicting Jobs
AAMAS '24: Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent SystemsMay 2024, Pages 2659–2667Allocating conflicting jobs among individuals while respecting a budget constraint for each individual is an optimization problem that arises in various real-world scenarios. In this paper, we consider the situation where each individual derives some ...
- ArticleSeptember 2023
- ArticleSeptember 2023
Degreewidth: A New Parameter for Solving Problems on Tournaments
Graph-Theoretic Concepts in Computer ScienceJun 2023, Pages 246–260https://doi.org/10.1007/978-3-031-43380-1_18AbstractIn the paper, we define a new parameter for tournaments called degreewidth which can be seen as a measure of how far is the tournament from being acyclic. The degreewidth of a tournament T denoted by is the minimum value k for which we can find ...
- research-articleFebruary 2023
Stable Matchings with Restricted Preferences: Structure and Complexity
ACM Transactions on Economics and Computation (TEAC), Volume 10, Issue 3Article No.: 13, Pages 1–45https://doi.org/10.1145/3565558In the stable marriage (SM) problem, there are two sets of agents—traditionally referred to as men and women—and each agent has a preference list that ranks (a subset of) agents of the opposite sex. The goal is to find a matching between men and women ...
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- research-articleOctober 2022
k-apices of Minor-closed Graph Classes. II. Parameterized Algorithms
ACM Transactions on Algorithms (TALG), Volume 18, Issue 3Article No.: 21, Pages 1–30https://doi.org/10.1145/3519028Let 𝒢 be a minor-closed graph class. We say that a graph G is a k-apex of 𝒢 if G contains a set S of at most k vertices such that G\S belongs to 𝒢. We denote by 𝒜k (𝒢) the set of all graphs that are k-apices of 𝒢. In the first paper of this series, ...
- research-articleJanuary 2022
A Linear Fixed Parameter Tractable Algorithm for Connected Pathwidth
SIAM Journal on Discrete Mathematics (SIDMA), Volume 36, Issue 1Mar 2022, Pages 411–435https://doi.org/10.1137/20M1369361The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search, where we are given a system of tunnels (represented by a graph) that is ...
- research-articleJuly 2021
Stable Matchings with Restricted Preferences: Structure and Complexity
EC '21: Proceedings of the 22nd ACM Conference on Economics and ComputationJuly 2021, Pages 319–339https://doi.org/10.1145/3465456.3467618It is well known that every stable matching instance I has a rotation poset R(I) that can be computed efficiently and the downsets of R(I) are in one-to-one correspondence with the stable matchings of I. Furthermore, for every poset P, an instance I(P) ...
- research-articleJanuary 2021
Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices
SIAM Journal on Discrete Mathematics (SIDMA), Volume 35, Issue 12021, Pages 546–574https://doi.org/10.1137/18M1209489We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parameterization. ...
- research-articleJune 2020
Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms
ACM Transactions on Algorithms (TALG), Volume 16, Issue 3Article No.: 32, Pages 1–31https://doi.org/10.1145/3379698We present two new combinatorial tools for the design of parameterized algorithms. The first is a simple linear time randomized algorithm that given as input a d-degenerate graph G and an integer k, outputs an independent set Y, such that for every ...
- research-articleJune 2020
Nearly ETH-tight Algorithms for Planar Steiner Tree with Terminals on Few Faces
ACM Transactions on Algorithms (TALG), Volume 16, Issue 3Article No.: 28, Pages 1–30https://doi.org/10.1145/3371389The STEINER TREE problem is one of the most fundamental NP-complete problems, as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights and a subset of vertices (often called terminals); the ...
- research-articleJanuary 2020
Bidimensionality and Kernels
SIAM Journal on Computing (SICOMP), Volume 49, Issue 62020, Pages 1397–1422https://doi.org/10.1137/16M1080264Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866--893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, Bidimensionality: New ...
- research-articleApril 2019
The treewidth of smart contracts
SAC '19: Proceedings of the 34th ACM/SIGAPP Symposium on Applied ComputingApril 2019, Pages 400–408https://doi.org/10.1145/3297280.3297322Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal ...
- research-articleJune 2017
Finding even cycles faster via capped k-walks
STOC 2017: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of ComputingJune 2017, Pages 112–120https://doi.org/10.1145/3055399.3055459Finding cycles in graphs is a fundamental problem in algorithmic graph theory. In this paper, we consider the problem of finding and reporting a cycle of length 2k in an undirected graph G with n nodes and m edges for constant k≥ 2. A classic result by ...
- research-articleMarch 2017
Representative Families of Product Families
ACM Transactions on Algorithms (TALG), Volume 13, Issue 3Article No.: 36, Pages 1–29https://doi.org/10.1145/3039243A subfamily F′ of a set family F is said to q-represent F if for every A ∈ F and B of size q such that A∩B = ∅ there exists a set A′ ∈ F′ such that A′ ∩ B = ∅. Recently, we provided an algorithm that, for a given family F of sets of size p together with ...
- research-articleJanuary 2017
Metric Dimension of Bounded Tree-length Graphs
SIAM Journal on Discrete Mathematics (SIDMA), Volume 31, Issue 22017, Pages 1217–1243https://doi.org/10.1137/16M1057383The notion of resolving sets in a graph was introduced by Slater [Proceedings of the Sixth Southeastern Conference on Combinatorics, Graph Theory, and Computing, Util. Math., Winnipeg, 1975, pp. 549--559] and Harary and Melter [Ars Combin., 2 (1976), pp. ...
- research-articleJanuary 2017
Hitting Selected (Odd) Cycles
SIAM Journal on Discrete Mathematics (SIDMA), Volume 31, Issue 32017, Pages 1581–1615https://doi.org/10.1137/15M1041213In the Subset Odd Cycle Transversal (Subset OCT) problem, the input is a graph $G$, a subset of vertices $T$ and a positive integer $k$ and the objective is to determine whether there exists a $k$-sized vertex subset that intersects every odd cycle ...
- research-articleJanuary 2017
Parameterized Complexity of Directed Steiner Tree on Sparse Graphs
SIAM Journal on Discrete Mathematics (SIDMA), Volume 31, Issue 22017, Pages 1294–1327https://doi.org/10.1137/15M103618XWe study the parameterized complexity of the directed variant of the classical Steiner Tree problem on various classes of directed sparse graphs. While the parameterized complexity of Steiner Tree parameterized by the number of terminals is well ...
- research-articleSeptember 2016
Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms
Journal of the ACM (JACM), Volume 63, Issue 4Article No.: 29, Pages 1–60https://doi.org/10.1145/2886094Let M=(E, I) be a matroid and let S={S1, ċ , St} be a family of subsets of E of size p. A subfamily Ŝ ⊆ S is q-representative for S if for every set Y⊆E of size at most q, if there is a set X ∈ S disjoint from Y with X∪ Y ∈ I, then there is a set Xˆ ∈ Ŝ ...