20 Search Results for "Orlin, James B."

Document
DOI: 10.4230/LIPIcs.STACS.2026.12
Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density

Authors: Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study τ-Bounded-Density Edge Deletion (τ-BDED), where given an undirected graph G, the task is to remove as few edges as possible to obtain a graph G' where no subgraph of G' has density more than τ. The density of a (sub)graph is the number of edges divided by the number of vertices. This problem was recently introduced and shown to be NP-hard for τ ∈ {2/3, 3/4, 1 + 1/25}, but polynomial-time solvable for τ ∈ {0,1/2,1} [Bazgan et al., JCSS 2025]. We provide a complete dichotomy with respect to the target density τ: 1) If 2τ ∈ ℕ (half-integral target density) or τ < 2/3, then τ-BDED is polynomial-time solvable. 2) Otherwise, τ-BDED is NP-hard. We complement the NP-hardness with fixed-parameter tractability with respect to the treewidth of G. Moreover, for integral target density τ ∈ ℕ, we show τ-BDED to be solvable in randomized O(m^{1 + o(1)}) time. Our algorithmic results are based on a reduction to a new general flow problem on restricted networks that, depending on τ, can be solved via Maximum s-t-Flow or General Factors. We believe this connection between these variants of flow and matching to be of independent interest.
Cite as

Matthias Bentert, Tom-Lukas Breitkopf, Vincent Froese, Anton Herrmann, and André Nichterlein. Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2026.12,
  author =	{Bentert, Matthias and Breitkopf, Tom-Lukas and Froese, Vincent and Herrmann, Anton and Nichterlein, Andr\'{e}},
  title =	{{Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.12},
  URN =		{urn:nbn:de:0030-drops-255012},
  doi =		{10.4230/LIPIcs.STACS.2026.12},
  annote =	{Keywords: Transshipment, Maximum Flow, General Factors, Matching, Graph Modification Problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.4
Pseudodeterministic Algorithms for Minimum Cut Problems

Authors: Aryan Agarwala and Nithin Varma

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
In this paper we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.
Cite as

Aryan Agarwala and Nithin Varma. Pseudodeterministic Algorithms for Minimum Cut Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.4,
  author =	{Agarwala, Aryan and Varma, Nithin},
  title =	{{Pseudodeterministic Algorithms for Minimum Cut Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.4},
  URN =		{urn:nbn:de:0030-drops-252917},
  doi =		{10.4230/LIPIcs.ITCS.2026.4},
  annote =	{Keywords: Minimum Cut, Pseudodeterministic Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.18
An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies

Authors: Yike Chen, Ke Shi, and Chao Xu

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

Abstract
The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its respective delivery point. The goal is to minimize the total distance traveled. SCP is known to be NP-hard, even on trees. The only positive results, in terms of polynomial-time solvability, apply to graphs that are topologically equivalent to a path or a cycle. We propose an algorithm that is optimal for each fixed topology, running in near-linear time. This is achieved by demonstrating that the problem is fixed-parameter tractable (FPT) when parameterized by both the cycle rank and the number of branch vertices.
Cite as

Yike Chen, Ke Shi, and Chao Xu. An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2025.18,
  author =	{Chen, Yike and Shi, Ke and Xu, Chao},
  title =	{{An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{18:1--18:12},
  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.2025.18},
  URN =		{urn:nbn:de:0030-drops-249269},
  doi =		{10.4230/LIPIcs.ISAAC.2025.18},
  annote =	{Keywords: Stacker Crane Problem, Fixed-Parameter Tractable, Min-Cost Circulation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.19
Traffic-Oblivious Multi-Commodity Flow Network Design

Authors: Markus Chimani and Max Ilsen

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

Abstract
We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph G with edge capacities cap and a retention ratio α ∈ (0,1), find an edge-wise minimum subgraph G' ⊆ G such that for all traffic matrices T routable in G using a multi-commodity flow, α⋅ T is routable in G'. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network. In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a max(1/α, 2)-approximation based on a surprisingly simple LP-rounding scheme. We also give instances where this worst-case approximation ratio is met and thus prove that our analysis is tight.
Cite as

Markus Chimani and Max Ilsen. Traffic-Oblivious Multi-Commodity Flow Network Design. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chimani_et_al:LIPIcs.ISAAC.2025.19,
  author =	{Chimani, Markus and Ilsen, Max},
  title =	{{Traffic-Oblivious Multi-Commodity Flow Network Design}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{19:1--19:17},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-249273},
  doi =		{10.4230/LIPIcs.ISAAC.2025.19},
  annote =	{Keywords: Multi-commodity flow, Digraphs, LP-rounding, Approximation algorithm}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.1
The Fair Periodic Assignment Problem

Authors: Rolf Nelson van Lieshout and Bartholomeüs Theodorus Cornelis van Rossum

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a 𝒪(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always be found using the Nearest Neighbor heuristic. We characterize all instances that admit a solution that is both fair and efficient, and use this result to develop a 𝒪(n log n) exact algorithm for the fair periodic assignment problem. Finally, we show that allowing aperiodic schedules never reduces the price of fairness.
Cite as

Rolf Nelson van Lieshout and Bartholomeüs Theodorus Cornelis van Rossum. The Fair Periodic Assignment Problem. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanlieshout_et_al:OASIcs.ATMOS.2025.1,
  author =	{van Lieshout, Rolf Nelson and van Rossum, Bartholome\"{u}s Theodorus Cornelis},
  title =	{{The Fair Periodic Assignment Problem}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{1:1--1:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.1},
  URN =		{urn:nbn:de:0030-drops-247574},
  doi =		{10.4230/OASIcs.ATMOS.2025.1},
  annote =	{Keywords: Cyclic scheduling, Fairness, Traveling Salesman Problem}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.55
Safe Sequences via Dominators in DAGs for Path-Covering Problems

Authors: Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this paper we study safe sequences of nodes or arcs, namely sequences that appear in some path of every path cover of a DAG. We show that safe sequences admit a simple characterization via cutnodes. Moreover, we establish a connection between maximal safe sequences and leaf-to-root paths in the source- and sink-dominator trees of the DAG, which may be of independent interest in the extensive literature on dominators. With dominator trees, safe sequences admit an O(n)-size representation and a linear-time output-sensitive enumeration algorithm running in time O(m + o), where n and m are the number of nodes and arcs, respectively, and o is the total length of the maximal safe sequences. We then apply maximal safe sequences to simplify Integer Linear Programs (ILPs) for two path-covering problems, LeastSquares and MinPathError, which are at the core of RNA transcript assembly problems from bioinformatics. On various datasets, maximal safe sequences can be computed in under 0.1 seconds per graph, on average, and ILP solvers whose search space is reduced in this manner exhibit significant speed-ups. For example on graphs with a large width, average speed-ups are in the range 50-250× for MinPathError and in the range 80-350× for LeastSquares. Optimizing ILPs using safe sequences can thus become a fast building block of practical RNA transcript assembly tools, and more generally, of path-covering problems.
Cite as

Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu. Safe Sequences via Dominators in DAGs for Path-Covering Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sena_et_al:LIPIcs.ESA.2025.55,
  author =	{Sena, Francisco and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Safe Sequences via Dominators in DAGs for Path-Covering Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.55},
  URN =		{urn:nbn:de:0030-drops-245230},
  doi =		{10.4230/LIPIcs.ESA.2025.55},
  annote =	{Keywords: directed acyclic graph, path cover, dominator tree, integer linear programming, least squares, minimum path error}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.68
Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut

Authors: Surender Baswana, Koustav Bhanja, and Anupam Roy

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Let G be a directed graph on n vertices and m edges. In this article, we study (s,t)-cuts of second minimum capacity and present the following algorithmic and graph-theoretic results. 1) Second (s,t)-mincut: Vazirani and Yannakakis [ICALP 1992] designed the first algorithm for computing an (s,t)-cut of second minimum capacity using {O}(n²) maximum (s,t)-flow computations. We present the following algorithm that improves the running time significantly. For directed integer-weighted graphs, there is an algorithm that can compute an (s,t)-cut of second minimum capacity using Õ(√n) maximum (s,t)-flow computations with high probability. To achieve this result, a close relationship of independent interest is established between (s,t)-cuts of second minimum capacity and global mincuts in directed weighted graphs. 2) Minimum+1 (s,t)-cuts: Minimum+1 (s,t)-cuts have been studied quite well recently [Baswana, Bhanja, and Pandey, ICALP 2022 & TALG 2023], which is a special case of second (s,t)-mincut. We present the following structural result and the first nontrivial algorithm for minimum+1 (s,t)-cuts. 3) Algorithm: For directed multi-graphs, we design an algorithm that, given any maximum (s,t)-flow, computes a minimum+1 (s,t)-cut, if it exists, in O(m) time. 4) Structure: The existing structures for storing and characterizing all minimum+1 (s,t)-cuts occupy {O}(mn) space [Baswana, Bhanja, and Pandey, TALG 2023]. For undirected multi-graphs, we design a directed acyclic graph (DAG) occupying only {O}(m) space that stores and characterizes all minimum+1 (s,t)-cuts. This matches the space bound of the widely-known DAG structure for all (s,t)-mincuts [Picard and Queyranne, Math. Prog. Studies 1980]. 5) Dual Edge Sensitivity Oracle: The study of minimum+1 (s,t)-cuts often turns out to be useful in designing dual edge sensitivity oracles - a compact data structure for efficiently reporting an (s,t)-mincut after insertion/failure of any given pair of query edges. It has been shown recently [Bhanja, ICALP 2025] that any dual edge sensitivity oracle for (s,t)-mincut in undirected multi-graphs must occupy Ω(n²) space in the worst-case irrespective of the query time. Interestingly, for undirected unweighted simple graphs, we break this quadratic barrier while achieving a non-trivial query time as follows. There is an O(n√n) space data structure that can report an (s,t)-mincut in O(min{m,n√n}) time after the insertion/failure of any given pair of query edges. To arrive at our results, as one of our key techniques, we establish interesting relationships between (s,t)-cuts of capacity (minimum+Δ), Δ ≥ 0, and maximum (s,t)-flow. We believe that these techniques and the graph-theoretic result in 2.(b) are of independent interest.
Cite as

Surender Baswana, Koustav Bhanja, and Anupam Roy. Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 68:1-68:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baswana_et_al:LIPIcs.ESA.2025.68,
  author =	{Baswana, Surender and Bhanja, Koustav and Roy, Anupam},
  title =	{{Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{68:1--68:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.68},
  URN =		{urn:nbn:de:0030-drops-245369},
  doi =		{10.4230/LIPIcs.ESA.2025.68},
  annote =	{Keywords: mincut, second mincut, compact structure, fault tolerant, sensitivity oracle, dual edges, st mincut, global mincut, characterization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.112
A Faster Parametric Search for the Integral Quickest Transshipment Problem

Authors: Mariia Anapolska, Dario van den Boom, Christina Büsing, and Timo Gersing

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, however, no structural improvements on their algorithm itself have yet been proposed. Runtime improvements are limited to general progress on submodular function minimization (SFM), which is an integral part of Hoppe and Tardos' algorithm. In fact, SFM constitutes the main computational load of the algorithm, as the runtime is blown up by using it within Megiddo’s parametric search algorithm. We replace this part of Hoppe and Tardos' algorithm with a more efficient routine that solves only a linear number of SFM and, in contrast to previous techniques, exclusively uses minimum cost flow algorithms within Megiddo’s parametric search. Our approach improves the state-of-the-art runtime from 𝒪̃(m⁴ k^15) down to 𝒪̃(m²k⁵ + m⁴ k²), where k is the number of terminals and m is the number of arcs.
Cite as

Mariia Anapolska, Dario van den Boom, Christina Büsing, and Timo Gersing. A Faster Parametric Search for the Integral Quickest Transshipment Problem. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anapolska_et_al:LIPIcs.ESA.2025.112,
  author =	{Anapolska, Mariia and van den Boom, Dario and B\"{u}sing, Christina and Gersing, Timo},
  title =	{{A Faster Parametric Search for the Integral Quickest Transshipment Problem}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.112},
  URN =		{urn:nbn:de:0030-drops-245817},
  doi =		{10.4230/LIPIcs.ESA.2025.112},
  annote =	{Keywords: Flow over time, dynamic transshipment, quickest transshipment, parametric submodular functions, efficient algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.43
Edge Clique Partition and Cover Beyond Independence

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of cliques in an edge cover or partition can be very close to the size of a maximum independent set α(G). Motivated by this observation, we investigate above-α parameterizations of the edge clique cover and partition problems. Concretely, we introduce and study Edge Clique Cover Above Independent Set (ECC/α) and Edge Clique Partition Above Independent Set (ECP/α), where the goal is to cover or partition all edges of a graph using at most α(G) + k cliques, and k is the parameter. Our main results reveal a distinct complexity landscape for the two variants. We show that ECP/α is fixed-parameter tractable, whereas ECC/α is NP-complete for all k ≥ 2, yet can be solved in polynomial time for k ∈ {0,1}. These findings highlight intriguing differences between the two problems when viewed through the lens of parameterization above a natural lower bound. Finally, we demonstrate that ECC/α becomes fixed-parameter tractable when parameterized by k + ω(G), where ω(G) is the size of a maximum clique of the graph G. This result is particularly relevant for sparse graphs, in which ω is typically small. For H-minor free graphs, we design a subexponential algorithm of running time f(H)^√k ⋅ n^𝒪(1).
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Edge Clique Partition and Cover Beyond Independence. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fomin_et_al:LIPIcs.ESA.2025.43,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Edge Clique Partition and Cover Beyond Independence}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.43},
  URN =		{urn:nbn:de:0030-drops-245113},
  doi =		{10.4230/LIPIcs.ESA.2025.43},
  annote =	{Keywords: edge clique partition, edge clique cover, independence number, parameterized complexity, above guarantee}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.77
Minimization of Deterministic Finite Automata Modulo the Edit Distance

Authors: Jakub Michaliszyn and Jan Otop

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

Abstract
We propose a novel approach to minimization of deterministic finite automata (DFA), in which the DFA is further minimized at the expense of relaxing equality of languages to merely a similarity. As the notion of similarity of languages, we consider the edit distance between languages ℒ, ℒ', i.e., the minimal number of edits necessary to transform any word from ℒ to some word from ℒ' and vice versa. In this paper we address two problems: minimization up to a predetermined edit distance given in the input, and minimization up to a bounded edit distance, in which there has to be an upper bound on the number of edits, but it is not specified. We show the first problem to be PSpace {}-complete and that the second problem is in Σ₂^p, and both NP-hard and coNP-hard. We show that if we limit how many strongly connected components can be visited by a single run (i.e., bounded SCC-depth), the problem becomes NP-complete. We also establish maximal subclasses of DFA over which minimization up to a bounded edit distance can be performed in polynomial time. Additionally, we provide a succinct overview of alternative metrics for assessing language similarity.
Cite as

Jakub Michaliszyn and Jan Otop. Minimization of Deterministic Finite Automata Modulo the Edit Distance. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 77:1-77:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{michaliszyn_et_al:LIPIcs.MFCS.2025.77,
  author =	{Michaliszyn, Jakub and Otop, Jan},
  title =	{{Minimization of Deterministic Finite Automata Modulo the Edit Distance}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{77:1--77:17},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-241843},
  doi =		{10.4230/LIPIcs.MFCS.2025.77},
  annote =	{Keywords: automata theory, automata minimization, edit distance}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.93
Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity

Authors: Jingyang Zhao and Mingyu Xiao

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

Abstract
The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In this paper, we consider k-CVRP in general metrics and on general graphs, where k is the vehicle capacity. All three versions are APX-hard for any fixed k ≥ 3. Assume that the approximation ratio of metric TSP is 3/2. We present a (5/2 - Θ(√{1/k}))-approximation algorithm for the splittable and unit-demand cases, and a (5/2 + ln 2 - Θ(√{1/k}))-approximation algorithm for the unsplittable case. Our approximation ratio is better than the previous results when k is less than a sufficiently large value, approximately 1.7 x 10⁷. For small values of k, we design independent and elegant algorithms with further improvements. For the splittable and unit-demand cases, we improve the approximation ratio from 1.792 to 1.500 for k = 3, and from 1.750 to 1.500 for k = 4. For the unsplittable case, we improve the approximation ratio from 1.792 to 1.500 for k = 3, from 2.051 to 1.750 for k = 4, and from 2.249 to 2.157 for k = 5. The approximation ratio for k = 3 surprisingly achieves the same value as in the splittable case. Our techniques, such as EX-ITP - an extension of the classic ITP method, have the potential to improve algorithms for other routing problems as well.
Cite as

Jingyang Zhao and Mingyu Xiao. Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 93:1-93:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zhao_et_al:LIPIcs.MFCS.2025.93,
  author =	{Zhao, Jingyang and Xiao, Mingyu},
  title =	{{Improved Approximation Algorithms for Capacitated Vehicle Routing with Fixed Capacity}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{93:1--93:19},
  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.2025.93},
  URN =		{urn:nbn:de:0030-drops-242008},
  doi =		{10.4230/LIPIcs.MFCS.2025.93},
  annote =	{Keywords: Combinatorial Optimization, Capacitated Vehicle Routing, Approximation Algorithms, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.10
Algorithm Engineering of SSSP with Negative Edge Weights

Authors: Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Aaron Bernstein et al., 2022] presented a randomized near-linear time algorithm for this problem. A subsequent improvement in [Karl Bringmann et al., 2023] significantly reduced the number of logarithmic factors and thereby also simplified the algorithm. It is surprising and exciting that both of these algorithms are combinatorial and do not contain any fundamental obstacles for being practical. We launch the, to the best of our knowledge, first extensive investigation towards a practical implementation of [Karl Bringmann et al., 2023]. To this end, we give an accessible overview of the algorithm and discuss what adaptions are necessary to obtain a fast algorithm in practice. We manifest these adaptions in an efficient implementation. We test our implementation on a benchmark data set that is adapted to be more difficult for our implementation in order to allow for a fair comparison. As in [Karl Bringmann et al., 2023] as well as in our implementation there are multiple parameters to tune, we empirically evaluate their effect and thereby determine the best choices. Our implementation is then extensively compared to one of the state-of-the-art algorithms for this problem [Andrew V. Goldberg and Tomasz Radzik, 1993]. On the hardest instance type, we are faster by up to almost two orders of magnitude.
Cite as

Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi. Algorithm Engineering of SSSP with Negative Edge Weights. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cassis_et_al:LIPIcs.SEA.2025.10,
  author =	{Cassis, Alejandro and Karrenbauer, Andreas and Nusser, Andr\'{e} and Rinaldi, Paolo Luigi},
  title =	{{Algorithm Engineering of SSSP with Negative Edge Weights}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.10},
  URN =		{urn:nbn:de:0030-drops-232486},
  doi =		{10.4230/LIPIcs.SEA.2025.10},
  annote =	{Keywords: Single Source Shortest Paths, Negative Weights, Near-Linear Time}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.45
Scarf’s Algorithm on Arborescence Hypergraphs

Authors: Karthekeyan Chandrasekaran, Yuri Faenza, Chengyue He, and Jay Sethuraman

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

Abstract
Scarf’s algorithm - a pivoting procedure that finds a dominating extreme point in a down-monotone polytope - can be used to show the existence of a fractional stable matching in hypergraphs. The problem of finding a fractional stable matching in hypergraphs, however, is PPAD-complete. In this work, we study the behavior of Scarf’s algorithm on arborescence hypergraphs, the family of hypergraphs in which hyperedges correspond to the paths of an arborescence. For arborescence hypergraphs, we prove that Scarf’s algorithm can be implemented to find an integral stable matching in polynomial time. En route to our result, we uncover novel structural properties of bases and pivots for the more general family of network hypergraphs. Our work provides the first proof of polynomial-time convergence of Scarf’s algorithm on hypergraphic stable matching problems, giving hope to the possibility of polynomial-time convergence of Scarf’s algorithm for other families of polytopes.
Cite as

Karthekeyan Chandrasekaran, Yuri Faenza, Chengyue He, and Jay Sethuraman. Scarf’s Algorithm on Arborescence Hypergraphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chandrasekaran_et_al:LIPIcs.ICALP.2025.45,
  author =	{Chandrasekaran, Karthekeyan and Faenza, Yuri and He, Chengyue and Sethuraman, Jay},
  title =	{{Scarf’s Algorithm on Arborescence Hypergraphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{45:1--45:18},
  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.2025.45},
  URN =		{urn:nbn:de:0030-drops-234220},
  doi =		{10.4230/LIPIcs.ICALP.2025.45},
  annote =	{Keywords: Scarf’s algorithm, Arborescence Hypergraphs, Stable Matchings}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.27
Minimum+1 Steiner Cut and Dual Edge Sensitivity Oracle: Bridging Gap between Global and (s,t)-cut

Authors: Koustav Bhanja

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

Abstract
Let G = (V,E) be an undirected multi-graph on n = |V| vertices and S ⊆ V be a Steiner set in G. Steiner cut is a fundamental concept; moreover, global cut (|S| = n), as well as (s,t)-cut (|S| = 2), is just a special case of Steiner cut. We study Steiner cuts of capacity minimum+1, and as an important application, we provide a dual edge Sensitivity Oracle for Steiner mincut - a compact data structure for efficiently reporting a Steiner mincut after failure/insertion of any pair of edges. A compact data structure for cuts of capacity minimum+1 has been designed for both global cuts [Dinitz and Nutov, STOC 1995] and (s,t)-cuts [Baswana, Bhanja, and Pandey, ICALP 2022 & TALG 2023]. Moreover, both data structures are also used crucially to design a dual edge Sensitivity Oracle for their respective mincuts. Unfortunately, except for these two extreme scenarios of Steiner cuts, no generalization of these results is known. Therefore, to address this gap, we present the following first results on Steiner cuts for any S satisfying 2 ≤ |S| ≤ n. 1) Data Structure for Minimum+1 Steiner Cut: There is an {O}(n(n-|S|+1)) space data structure that, given any pair of vertices u,v, can determine in {O}(1) time whether the Steiner cut of the least capacity separating u and v has capacity minimum+1. It can report such a cut, if it exists, in {O}(n) time, which is worst-case optimal. 2) Dual Edge Sensitivity Oracle: We design the following pair of data structures. (a) There is an {O}(n(n-|S|+1)) space data structure that, after the failure or insertion of any pair of edges in G, can report the capacity of Steiner mincut in {O}(1) time and a Steiner mincut in {O}(n) time, which is worst-case optimal. (b) If we are interested in reporting only the capacity of Steiner mincut, there is a more compact data structure that occupies {O}((n-|S|)²+n) space and can report the capacity of Steiner mincut in {O}(1) time after the failure or insertion of any pair of edges. 3) Lower Bound for Sensitivity Oracle: For undirected multi-graphs, for any Steiner set S ⊆ V, any data structure that, after the failure or insertion of any pair of edges, can report the capacity of Steiner mincut must occupy Ω((n-|S|)²) bits of space in the worst case, irrespective of the query time. To arrive at our results, we provide several techniques, especially a generalization of the 3-Star Lemma given by Dinitz and Vainshtein [SICOMP 2000], which is of independent interest. Our results achieve the same space and time bounds of the existing results for the two extreme scenarios of Steiner cuts - global and (s,t)-cut. In addition, the space occupied by our data structures in (1) and (2) reduces as |S| tends to n. Also, they occupy subquadratic space if |S| is close to n.
Cite as

Koustav Bhanja. Minimum+1 Steiner Cut and Dual Edge Sensitivity Oracle: Bridging Gap between Global and (s,t)-cut. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhanja:LIPIcs.ICALP.2025.27,
  author =	{Bhanja, Koustav},
  title =	{{Minimum+1 Steiner Cut and Dual Edge Sensitivity Oracle: Bridging Gap between Global and (s,t)-cut}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{27:1--27:20},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-234040},
  doi =		{10.4230/LIPIcs.ICALP.2025.27},
  annote =	{Keywords: cut, mincut, minimum+1, steiner, edge fault, sensitivity oracle, dual edges}
}
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