19 Search Results for "Elbassioni, Khaled"

Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.31
Token Sliding Independent Set Reconfiguration on Block Graphs

Authors: Mathew C. Francis and Veena Prabhakaran

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Let S be an independent set of a simple undirected graph G. Suppose that each vertex of S has a token placed on it. The tokens are allowed to be moved, one at a time, by sliding along the edges of G while maintaining the property that after each move, the vertices having tokens always form an independent set of G. We would like to determine whether the tokens can be eventually brought to stay on the vertices of another independent set S' of G in this manner. In other words, we would like to decide if we can transform S into S' through a sequence of steps, each of which involves substituting a vertex in the current independent set with one of its neighbours to obtain another independent set. This problem of determining if one independent set of a graph "is reachable" from another independent set of it is known to be PSPACE-hard even for split graphs, planar graphs, and graphs of bounded treewidth. Polynomial time algorithms have been obtained for certain graph classes like trees, interval graphs, claw-free graphs, and bipartite permutation graphs. We present a polynomial time algorithm for the problem on block graphs, which are the graphs in which every maximal 2-connected subgraph is a clique. Our algorithm is the first generalization of the known polynomial time algorithm for trees to a larger class of graphs.
Cite as

Mathew C. Francis and Veena Prabhakaran. Token Sliding Independent Set Reconfiguration on Block Graphs. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{francis_et_al:LIPIcs.FSTTCS.2025.31,
  author =	{Francis, Mathew C. and Prabhakaran, Veena},
  title =	{{Token Sliding Independent Set Reconfiguration on Block Graphs}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.31},
  URN =		{urn:nbn:de:0030-drops-251120},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.31},
  annote =	{Keywords: Token sliding independent set reconfiguration, block graphs, polynomial time algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.24
Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree

Authors: Oscar Defrain, Arthur Ohana, and Simon Vilmin

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We consider the problem of enumerating the irreducible closed sets of a closure system given by an implicational base. To date, the complexity status of this problem is widely open, and it is further known to generalize the notorious hypergraph dualization problem, even in the case of acyclic convex geometries, i.e., closure systems admitting an acyclic implicational base. This paper studies this case with a focus on the degree, which corresponds to the maximal number of implications in which an element occurs. We show that the problem is tractable for bounded values of this parameter, even when relaxed to the notions of premise- and conclusion-degree. Our algorithms rely on a sequential approach leveraging from acyclicity, combined with the solution graph traversal technique for the case of premise-degree. They are shown to perform in incremental-polynomial time. These results are complemented in the long version of this document by showing that the dual problem of constructing the implicational base can be solved in polynomial time. Finally, we argue that our running times cannot be improved to polynomial delay using the standard framework of flashlight search.
Cite as

Oscar Defrain, Arthur Ohana, and Simon Vilmin. Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{defrain_et_al:LIPIcs.ISAAC.2025.24,
  author =	{Defrain, Oscar and Ohana, Arthur and Vilmin, Simon},
  title =	{{Enumerating the Irreducible Closed Sets of an Acyclic Implicational Base of Bounded Degree}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.24},
  URN =		{urn:nbn:de:0030-drops-249321},
  doi =		{10.4230/LIPIcs.ISAAC.2025.24},
  annote =	{Keywords: Algorithmic enumeration, closure systems, acyclic convex geometries, solution graph traversal, flashlight search, extension, hypergraph dualization}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.15
Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs

Authors: Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Enumerating minimal dominating sets with polynomial delay in bipartite graphs is a long-standing open problem. To date, even the subcase of chordal bipartite graphs is open, with the best known algorithm due to Golovach, Heggernes, Kanté, Kratsch, Sæther, and Villanger running in incremental-polynomial time. We improve on this result by providing a polynomial delay and space algorithm enumerating minimal dominating sets in chordal bipartite graphs. Additionally, we show that the total and connected variants admit polynomial and incremental-polynomial delay algorithms, respectively, within the same class. This provides an alternative proof of a result by Golovach et al. for total dominating sets, and answers an open question for the connected variant. Finally, we give evidence that the techniques used in this paper cannot be generalized to bipartite graphs for (total) minimal dominating sets, unless P = NP, and show that enumerating minimal connected dominating sets in bipartite graphs is harder than enumerating minimal transversals in general hypergraphs.
Cite as

Emanuel Castelo, Oscar Defrain, and Guilherme C. M. Gomes. Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{castelo_et_al:LIPIcs.WADS.2025.15,
  author =	{Castelo, Emanuel and Defrain, Oscar and C. M. Gomes, Guilherme},
  title =	{{Enumerating Minimal Dominating Sets and Variants in Chordal Bipartite Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.15},
  URN =		{urn:nbn:de:0030-drops-242467},
  doi =		{10.4230/LIPIcs.WADS.2025.15},
  annote =	{Keywords: algorithmic enumeration, minimal dominating sets, connected dominating sets, total dominating sets, chordal bipartite graphs, sequential method, polynomial delay}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.19
On the Enumeration of Signatures of XOR-CNF’s

Authors: Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a CNF formula φ with clauses C_1, … , C_m over a set of variables V, a truth assignment 𝐚: V → {0, 1} generates a binary sequence σ_φ(𝐚) = (C_1(𝐚), …, C_m(𝐚)), called a signature of φ, where C_i(𝐚) = 1 if clause C_i evaluates to 1 under assignment 𝐚, and C_i(𝐚) = 0 otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, Bérczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNF’s.
Cite as

Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin. On the Enumeration of Signatures of XOR-CNF’s. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{creignou_et_al:LIPIcs.WADS.2025.19,
  author =	{Creignou, Nadia and Defrain, Oscar and Olive, Fr\'{e}d\'{e}ric and Vilmin, Simon},
  title =	{{On the Enumeration of Signatures of XOR-CNF’s}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.19},
  URN =		{urn:nbn:de:0030-drops-242508},
  doi =		{10.4230/LIPIcs.WADS.2025.19},
  annote =	{Keywords: Algorithmic enumeration, XOR-CNF, signatures, maximal bipartite subgraphs enumeration, extension, proximity search}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.44
Streaming Algorithms for Conflict-Free Coloring

Authors: Rogers Mathew, Fahad Panolan, and Seshikanth

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Conflict-free coloring of a hypergraph ℋ = (V,ℰ) using k colors is a function f:V → {1,2, …, k} such that for all E ∈ ℰ, there exists a vertex v ∈ E with a unique color. That is, f(v)≠ f(u) for all u ∈ E ⧵ {v}. The minimum k for which ℋ has a conflict-free coloring using k colors is called the conflict-free chromatic number of ℋ. For a simple graph G, a conflict-free coloring of the hypergraph with vertex set V(G) and edge set being the set of all closed neighborhoods of the vertices in G is called a conflict-free closed neighborhood (CFCN) coloring of G. CFCN chromatic number, denoted by χ_{CN}(G), is the minimum number of colors used in a conflict-free closed neighborhood coloring of G. Analogously, we define conflict-free open neighborhood (CFON) coloring and CFON chromatic number, χ_{ON}(G), of a graph G. There are various works on proving upper and lower bounds of χ_{ON}(G) and χ_{CN}(G). In this work, we develop streaming algorithms for CFCN and CFON coloring of a graph where the number of colors used matches the best-known upper bounds of χ_{ON}(G) and χi_{CN}(G). Our algorithms use as input an edge stream of the graph G in the insertion-only model. Our results and the best-known bounds for χ_{ON}(G) and χ_{CN}(G) are given below. 1. Pach and Tardos [Combinatorics, Probability and Computing, 2009] showed that, for any n vertex graph G, χ_{CN}(G) = O(ln² n). Glebov, Szabó and Tardos [Combinatorics, Probability and Computing, 2014] showed the existence of graphs G with χ_{CN}(G) = Ω(ln² n). We design a randomized single-pass semi-streaming algorithm (i.e., it uses O(n ln n) space that, given an n-vertex graph G, outputs a CFCN coloring of G using O(ln² n) colors with probability at least (1-2/n). 2. Bhyravarapu, Kalyanasundaram, Mathew [Journal of Graph Theory, 2021] showed that for a graph G with maximum degree Δ, χ_{CN}(G) = O(ln² Δ). The methods used by our algorithms give rise to a simpler, alternate proof for this bound. 3. It is known that χ_{ON}(G) ≤ 1/2 + √{2n + 1/4} (See Pach and Tardos [Combinatorics, Probability and Computing, 2009] and Ph.D. thesis of Cheilaris). This bound is asymptotically tight. - We design a deterministic single-pass O(n√n) space streaming algorithm that, given a graph G on n vertices, finds a CFON coloring using 2√n colors. - We design a randomized, single-pass, semi-streaming algorithm to find a CFON coloring of a graph G using O(√n ln² n) colors with success probability at least (1-2/n). 4. It is known that χ_{ON}(G) ≤ Δ+1, where Δ is the maximum degree of a vertex in G. Further, there are graphs G known with χ_{ON}(G) = Δ + 1. We design a randomized two-pass semi-streaming algorithm (uses O(1/(ε²) n ln³ n) space) that outputs a CFON coloring of G using (1+ε)Δ colors, for any ε > 0, with a probability at least (1-1/n).
Cite as

Rogers Mathew, Fahad Panolan, and Seshikanth. Streaming Algorithms for Conflict-Free Coloring. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mathew_et_al:LIPIcs.WADS.2025.44,
  author =	{Mathew, Rogers and Panolan, Fahad and Seshikanth},
  title =	{{Streaming Algorithms for Conflict-Free Coloring}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{44:1--44:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.44},
  URN =		{urn:nbn:de:0030-drops-242756},
  doi =		{10.4230/LIPIcs.WADS.2025.44},
  annote =	{Keywords: Streaming algorithm, conflict-free coloring, vertex coloring, randomized algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.33
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization

Authors: Jean Cardinal, Xavier Goaoc, and Sarah Wajsbrot

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new variants of these problems, dealing with continuous families of convex polyhedra, and show that they capture decision versions of the two-level finite adaptability problem in robust optimization. We show that these problems can be solved in strongly polynomial time when the size of the hitting/covering set and the dimension of the polyhedra and the parameter space are constant. We also show that the hitting set problem can be solved in strongly quadratic time for one-parameter families of convex polyhedra in constant dimension. This leads to new tractability results for finite adaptability that are the first ones with so-called left-hand-side uncertainty, where the underlying problem is non-linear.
Cite as

Jean Cardinal, Xavier Goaoc, and Sarah Wajsbrot. Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cardinal_et_al:LIPIcs.MFCS.2025.33,
  author =	{Cardinal, Jean and Goaoc, Xavier and Wajsbrot, Sarah},
  title =	{{Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.33},
  URN =		{urn:nbn:de:0030-drops-241401},
  doi =		{10.4230/LIPIcs.MFCS.2025.33},
  annote =	{Keywords: Geometric hitting set problem, Continuous families of polyhedra, Robust optimization}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.19
Designing Output Sensitive Algorithms for Subgraph Enumeration

Authors: Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
The enumeration of all subgraphs respecting some structural property is a fundamental task in theoretical computer science, with practical applications in many branches of data mining and network analysis. It is often of interest to only consider solutions (subgraphs) that are maximal under inclusion, and to achieve output-sensitive complexity, i.e., bounding the running time with respect to the number of subgraphs produced. In this paper, we provide a survey of techniques for designing output-sensitive algorithms for subgraph enumeration, including partition-based approaches such as flashlight search, solution-graph traversal methods such as reverse search, and cost amortization strategies such as push-out amortization. We also briefly discuss classes of efficiency, hardness of enumeration, and variants such as approximate enumeration. The paper is meant as an accessible handbook for learning the basics of the field and as a practical reference for selecting state-of-the-art subgraph enumeration strategies fitting to one’s needs.
Cite as

Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa. Designing Output Sensitive Algorithms for Subgraph Enumeration. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 19:1-19:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{conte_et_al:OASIcs.Grossi.19,
  author =	{Conte, Alessio and Kurita, Kazuhiro and Marino, Andrea and Punzi, Giulia and Uno, Takeaki and Wasa, Kunihiro},
  title =	{{Designing Output Sensitive Algorithms for Subgraph Enumeration}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{19:1--19:40},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.19},
  URN =		{urn:nbn:de:0030-drops-238180},
  doi =		{10.4230/OASIcs.Grossi.19},
  annote =	{Keywords: Graph algorithms, Graph enumeration, Output sensitive enumeration}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.145
Reducing Stochastic Games to Semidefinite Programming

Authors: Manuel Bodirsky, Georg Loho, and Mateusz Skomra

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a polynomial-time reduction from max-average constraints to the feasibility problem for semidefinite programs. This shows that Condon’s simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.
Cite as

Manuel Bodirsky, Georg Loho, and Mateusz Skomra. Reducing Stochastic Games to Semidefinite Programming. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 145:1-145:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodirsky_et_al:LIPIcs.ICALP.2025.145,
  author =	{Bodirsky, Manuel and Loho, Georg and Skomra, Mateusz},
  title =	{{Reducing Stochastic Games to Semidefinite Programming}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{145:1--145:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.145},
  URN =		{urn:nbn:de:0030-drops-235224},
  doi =		{10.4230/LIPIcs.ICALP.2025.145},
  annote =	{Keywords: Mean-payoff games, stochastic games, semidefinite programming, max-average constraints, max-atom problem}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.53
A PTAS for TSP with Neighbourhoods over Parallel Line Segments

Authors: Benyamin Ghaseminia and Mohammad R. Salavatipour

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We consider the Travelling Salesman Problem with Neighbourhoods (TSPN) on the Euclidean plane (ℝ²) and present a Polynomial-Time Approximation Scheme (PTAS) when the neighbourhoods are parallel line segments with lengths between [1, λ] for any constant value λ ≥ 1. In TSPN (which generalizes classic TSP), each client represents a set (or neighbourhood) of points in a metric and the goal is to find a minimum cost TSP tour that visits at least one point from each client set. In the Euclidean setting, each neighbourhood is a region on the plane. TSPN is significantly more difficult than classic TSP even in the Euclidean setting, as it captures group TSP. A notable case of TSPN is when each neighbourhood is a line segment. Although there are PTASs for when neighbourhoods are fat objects (with limited overlap), TSPN over line segments is APX-hard even if all the line segments have unit length. For parallel (unit) line segments, the best approximation factor is 3√2 from more than two decades ago. The PTAS we present in this paper settles the approximability of this case of the problem. Our algorithm finds a (1 + ε)-factor approximation for an instance of the problem for n segments with lengths in [1,λ] in time n^O(λ/ε³).
Cite as

Benyamin Ghaseminia and Mohammad R. Salavatipour. A PTAS for TSP with Neighbourhoods over Parallel Line Segments. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 53:1-53:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghaseminia_et_al:LIPIcs.SoCG.2025.53,
  author =	{Ghaseminia, Benyamin and Salavatipour, Mohammad R.},
  title =	{{A PTAS for TSP with Neighbourhoods over Parallel Line Segments}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{53:1--53:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.53},
  URN =		{urn:nbn:de:0030-drops-232058},
  doi =		{10.4230/LIPIcs.SoCG.2025.53},
  annote =	{Keywords: Approximation Scheme, TSP Neighbourhood, Parallel line segments}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.9
Spanner Enumeration for Temporal Graphs

Authors: Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.
Cite as

Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kurita_et_al:LIPIcs.SAND.2025.9,
  author =	{Kurita, Kazuhiro and Marino, Andrea and Schoeters, Jason and Uno, Takeaki},
  title =	{{Spanner Enumeration for Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.9},
  URN =		{urn:nbn:de:0030-drops-230621},
  doi =		{10.4230/LIPIcs.SAND.2025.9},
  annote =	{Keywords: temporal graphs, temporal spanners, one-to-all connectivity, all-to-all connectivity enumeration, NP-completeness, Dual-hardness, binary partition tree, flashlight search, polynomial delay}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.8
Enumeration of Minimal Hitting Sets Parameterized by Treewidth

Authors: Batya Kenig and Dan Shlomo Mizrahi

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
Enumerating the minimal hitting sets of a hypergraph is a problem which arises in many data management applications that include constraint mining, discovering unique column combinations, and enumerating database repairs. Previously, Eiter et al. [Thomas Eiter et al., 2003] showed that the minimal hitting sets of an n-vertex hypergraph, with treewidth w, can be enumerated with delay O^*(n^w) (ignoring polynomial factors), with space requirements that scale with the output size. We improve this to fixed-parameter-linear delay, following an FPT preprocessing phase. The memory consumption of our algorithm is exponential with respect to the treewidth of the hypergraph.
Cite as

Batya Kenig and Dan Shlomo Mizrahi. Enumeration of Minimal Hitting Sets Parameterized by Treewidth. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kenig_et_al:LIPIcs.ICDT.2025.8,
  author =	{Kenig, Batya and Mizrahi, Dan Shlomo},
  title =	{{Enumeration of Minimal Hitting Sets Parameterized by Treewidth}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.8},
  URN =		{urn:nbn:de:0030-drops-229498},
  doi =		{10.4230/LIPIcs.ICDT.2025.8},
  annote =	{Keywords: Enumeration, Hitting sets}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.43
Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programs

Authors: Khaled Elbassioni and Kazuhisa Makino

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular structure of this class of problems, to obtain more efficient algorithms than those offered by general SDP solvers. For certain applications, such as those described in this paper, it maybe required to deal with SDP’s with exponentially or infinitely many constraints, which are accessible only via an oracle. In this paper, we give an efficient primal-dual algorithm to solve the problem in this case, which is an extension of a logarithmic-potential based algorithm of Grigoriadis, Khachiyan, Porkolab and Villavicencio (SIAM Journal of Optimization 41 (2001)) for packing/covering linear programs.
Cite as

Khaled Elbassioni and Kazuhisa Makino. Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{elbassioni_et_al:LIPIcs.ESA.2019.43,
  author =	{Elbassioni, Khaled and Makino, Kazuhisa},
  title =	{{Oracle-Based Primal-Dual Algorithms for Packing and Covering Semidefinite Programs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.43},
  URN =		{urn:nbn:de:0030-drops-111642},
  doi =		{10.4230/LIPIcs.ESA.2019.43},
  annote =	{Keywords: Semidefinite programs, packing and covering, logarithmic potential, primal-dual algorithms, approximate solutions}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2018.18
Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices

Authors: Khaled Elbassioni and Kazuhisa Makino

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Abstract
We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron P=P(A,1_)={x in R^n | Ax >= 1_, x >= 0_}, when A is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour's decomposition of totally unimodular matrices, and may be of independent interest.
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Khaled Elbassioni and Kazuhisa Makino. Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{elbassioni_et_al:LIPIcs.SWAT.2018.18,
  author =	{Elbassioni, Khaled and Makino, Kazuhisa},
  title =	{{Enumerating Vertices of 0/1-Polyhedra associated with 0/1-Totally Unimodular Matrices}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.18},
  URN =		{urn:nbn:de:0030-drops-88441},
  doi =		{10.4230/LIPIcs.SWAT.2018.18},
  annote =	{Keywords: Totally unimodular matrices, Vertices of polyhedra, Vertex enumeration, Hypergraph transversals, Hypergraph decomposition, Output polynomial-time algorithm}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2017.40
Finding Small Hitting Sets in Infinite Range Spaces of Bounded VC-Dimension

Authors: Khaled Elbassioni

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
We consider the problem of finding a small hitting set in an infinite range space F=(Q,R) of bounded VC-dimension. We show that, under reasonably general assumptions, the infinite-dimensional convex relaxation can be solved (approximately) efficiently by multiplicative weight updates. As a consequence, we get an algorithm that finds, for any delta>0, a set of size O(s_F(z^*_F)) that hits (1-delta)-fraction of R (with respect to a given measure) in time proportional to log(1/delta), where s_F(1/epsilon) is the size of the smallest epsilon-net the range space admits, and z^*_F is the value of the fractional optimal solution. This exponentially improves upon previous results which achieve the same approximation guarantees with running time proportional to poly(1/delta). Our assumptions hold, for instance, in the case when the range space represents the visibility regions of a polygon in the plane, giving thus a deterministic polynomial-time O(log z^*_F)-approximation algorithm for guarding (1-delta)-fraction of the area of any given simple polygon, with running time proportional to polylog(1/delta).
Cite as

Khaled Elbassioni. Finding Small Hitting Sets in Infinite Range Spaces of Bounded VC-Dimension. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{elbassioni:LIPIcs.SoCG.2017.40,
  author =	{Elbassioni, Khaled},
  title =	{{Finding Small Hitting Sets in Infinite Range Spaces of Bounded VC-Dimension}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.40},
  URN =		{urn:nbn:de:0030-drops-72289},
  doi =		{10.4230/LIPIcs.SoCG.2017.40},
  annote =	{Keywords: VC-dimension, approximation algorithms, fractional covering, multiplicative weights update, art gallery problem, polyhedral separators, geometric cove}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.12
Exact Algorithms for List-Coloring of Intersecting Hypergraphs

Authors: Khaled Elbassioni

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
We show that list-coloring for any intersecting hypergraph of m edges on n vertices, and lists drawn from a set of size at most k, can be checked in quasi-polynomial time (mn)^{o(k^2*log(mn))}.
Cite as

Khaled Elbassioni. Exact Algorithms for List-Coloring of Intersecting Hypergraphs. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{elbassioni:LIPIcs.IPEC.2016.12,
  author =	{Elbassioni, Khaled},
  title =	{{Exact Algorithms for List-Coloring of Intersecting Hypergraphs}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.12},
  URN =		{urn:nbn:de:0030-drops-69444},
  doi =		{10.4230/LIPIcs.IPEC.2016.12},
  annote =	{Keywords: Hypergraph coloring, monotone Boolean duality, list coloring, exact algorithms, quasi-polynomial time}
}
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