32 Search Results for "Nagamochi, Hiroshi"

Document
DOI: 10.4230/LIPIcs.SEA.2026.21
An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem

Authors: Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
In this paper, we perform an experimental study of approximation algorithms for the unweighted tree augmentation problem (UTAP). Our goal is to establish a baseline performance for several existing approximation algorithms on actual instances rather than worst-case instances. In particular, we are interested in whether the algorithms' performance in practical instances is consistent with their worst-case guarantee rankings. We are also interested in whether preprocessing times, implementation difficulties, and running times justify the use of an algorithm in practice. We profile and analyze three approximation algorithms from the literature against a simple randomized algorithm. The performance of each algorithm was evaluated using metrics for space usage, running time, and solution quality. We found that the simple randomized algorithm is very competitive with the approximation algorithms and that the algorithms do not necessarily rank according to their theoretical guarantees. The randomized algorithm is easier to implement and understand, using less space than any of the more sophisticated approximation algorithms.
Cite as

Luke Hawranick, Matthew Williamson, Jacob Restanio, K. Subramani, and Cody Klingler. An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hawranick_et_al:LIPIcs.SEA.2026.21,
  author =	{Hawranick, Luke and Williamson, Matthew and Restanio, Jacob and Subramani, K. and Klingler, Cody},
  title =	{{An Empirical Analysis of Approximation Algorithms for the Unweighted Tree Augmentation Problem}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.21},
  URN =		{urn:nbn:de:0030-drops-260259},
  doi =		{10.4230/LIPIcs.SEA.2026.21},
  annote =	{Keywords: Graphs, Networks, Tree Augmentation, Approximation Algorithms, Empirical}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.36
Upward Book Embeddings of Partitioned Digraphs

Authors: Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a topological order and the edges are partitioned into pages, so that no two edges in the same page cross. For a partitioned digraph G = (V, ⋃^k_{i=1} E_i), that is, a digraph whose edge set is partitioned into k subsets, an upward book embedding is required to assign edges to pages as prescribed by the given partition. In a companion paper, Heath and Pemmaraju [SIAM J. Comput. 28(5), 1999] proved that the problem of testing the existence of an upward book embedding of a partitioned digraph is linear-time solvable for k = 1 and recently Akitaya, Demaine, Hesterberg, and Liu [GD, 2017] have shown the problem NP-complete for k ≥ 3. In this paper, we study upward book embeddings of partitioned digraphs and focus on the unsolved case k = 2. Our first main result is a novel characterization of the upward embeddings that support an upward book embedding in two pages. We exploit this characterization in several ways, and obtain a rich picture of the complexity landscape of the problem. First, we show that the problem remains NP-complete when k = 2, thus closing the complexity gap for the problem. Second, we show that, for an n-vertex partitioned digraph with a prescribed planar embedding, the existence of an upward book embedding that respects the given planar embedding can be tested in O(n log³ n) time. Finally, leveraging the SPQ(R)-tree decomposition of biconnected graphs into triconnected components, we present a cubic-time testing algorithm for biconnected directed partial 2-trees.
Cite as

Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter. Upward Book Embeddings of Partitioned Digraphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dalozzo_et_al:LIPIcs.SoCG.2026.36,
  author =	{Da Lozzo, Giordano and Frati, Fabrizio and Rutter, Ignaz},
  title =	{{Upward Book Embeddings of Partitioned Digraphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36},
  URN =		{urn:nbn:de:0030-drops-258424},
  doi =		{10.4230/LIPIcs.SoCG.2026.36},
  annote =	{Keywords: upward book embeddings, partitioned digraphs, SPQ-trees, 2-trees}
}
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
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2025.36
PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem

Authors: Florian Fontan and Guillaume Verger

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
In this paper, we describe the solver we submitted for both heuristic tracks of the PACE challenge 2025 on the dominating set problem and the hitting set problem. We solve both problems as unicost set covering problems. Our solver first performs reductions on the instance. Then greedy algorithms generate an initial solution that serves as starting point of the large neighborhood search and the local search which are executed afterwards. The solver ranked first in the dominating set heuristic track, and second in the hitting set heuristic track.
Cite as

Florian Fontan and Guillaume Verger. PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 36:1-36:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fontan_et_al:LIPIcs.IPEC.2025.36,
  author =	{Fontan, Florian and Verger, Guillaume},
  title =	{{PACE Solver Description: Reductions and Heuristic Search for the Dominating Set Problem and the Hitting Set Problem}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{36:1--36:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.36},
  URN =		{urn:nbn:de:0030-drops-251681},
  doi =		{10.4230/LIPIcs.IPEC.2025.36},
  annote =	{Keywords: dominating set, hitting set, unicost set covering, reductions, large neighborhood search, local search}
}
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/LIPIcs.GD.2025.23
The Price of Connectivity Augmentation on Planar Graphs

Authors: Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. Tóth, and Torsten Ueckerdt

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Given two classes of graphs, 𝒢₁ ⊆ 𝒢₂, and a c-connected graph G ∈ 𝒢₁, we wish to augment G with a smallest cardinality set of new edges F to obtain a k-connected graph G' = (V,E∪ F) ∈ 𝒢₂. In general, this is the c → k connectivity augmentation problem. Previous research considered variants where 𝒢₁ = 𝒢₂ is the class of planar graphs, plane graphs, or planar straight-line graphs. In all three settings, we prove that the c → k augmentation problem is NP-complete when 2 ≤ c < k ≤ 5. However, the connectivity of the augmented graph G' is at most 5 if 𝒢₂ is limited to planar graphs. We initiate the study of the c → k connectivity augmentation problem for arbitrary k ∈ ℕ, where 𝒢₁ is the class of planar graphs, plane graphs, or planar straight-line graphs, and 𝒢₂ is a beyond-planar class of graphs: 𝓁-planar, 𝓁-plane topological, or 𝓁-plane geometric graphs. We obtain tight bounds on the tradeoffs between the desired connectivity k and the local crossing number 𝓁 of the augmented graph G'. We also show that our hardness results apply to this setting. The connectivity augmentation problem for triangulations is intimately related to edge flips; and the minimum augmentation problem to the flip distance between triangulations. We prove that it is NP-complete to find the minimum flip distance between a given triangulation and a 4-connected triangulation, settling an open problem posed in 2014, and present an EPTAS for this problem.
Cite as

Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. Tóth, and Torsten Ueckerdt. The Price of Connectivity Augmentation on Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{a.akitaya_et_al:LIPIcs.GD.2025.23,
  author =	{A. Akitaya, Hugo and Dallant, Justin and Demaine, Erik D. and Kaufmann, Michael and Kleist, Linda and Stock, Frederick and T\'{o}th, Csaba D. and Ueckerdt, Torsten},
  title =	{{The Price of Connectivity Augmentation on Planar Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.23},
  URN =		{urn:nbn:de:0030-drops-250095},
  doi =		{10.4230/LIPIcs.GD.2025.23},
  annote =	{Keywords: connectivity augmentation, local crossing number, flip distance}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.7
On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits

Authors: Matthias Artmann, Andreas Padalkin, and Christian Scheideler

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
In programmable matter, we consider a large number of tiny, primitive computational entities called particles that run distributed algorithms to control global properties of the particle structure. Shape formation problems, where the particles have to reorganize themselves into a desired shape using basic movement abilities, are particularly interesting. In the related shape containment problem, the particles are given the description of a shape S and have to find maximally scaled representations of S within the initial configuration, without movements. For example, if S is a triangle, they have to identify the largest subsets of particles that already form a triangle. While the shape formation problem is being studied extensively, no attention has been given to the shape containment problem, which may have additional uses besides shape formation, such as detecting structural flaws. In this paper, we consider the shape containment problem within the geometric amoebot model for programmable matter, using its reconfigurable circuit extension to enable the instantaneous transmission of primitive signals on connected subsets of particles. We first prove a lower runtime bound of Ω (√n) synchronous rounds for the general problem, where n is the number of particles. Then, we present simple and efficient primitives for identifying subsets that form the desired shape. Using these primitives, we construct a large class of shapes which we call snowflakes. This class contains, among others, all shapes composed of parallelograms and hexagons, and the class of star convex shapes. Let k be the maximum scale of the considered shape in a given amoebot structure. If the shape is star convex, we solve it within 𝒪 (log² k) rounds. If it is a snowflake but not star convex, we solve it within 𝒪 (√n log n) rounds.
Cite as

Matthias Artmann, Andreas Padalkin, and Christian Scheideler. On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{artmann_et_al:LIPIcs.DISC.2025.7,
  author =	{Artmann, Matthias and Padalkin, Andreas and Scheideler, Christian},
  title =	{{On the Shape Containment Problem Within the Amoebot Model with Reconfigurable Circuits}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.7},
  URN =		{urn:nbn:de:0030-drops-248240},
  doi =		{10.4230/LIPIcs.DISC.2025.7},
  annote =	{Keywords: Programmable matter, amoebot model, reconfigurable circuits, shape containment}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.26
Faster Dynamic 2-Edge Connectivity in Directed Graphs

Authors: Loukas Georgiadis, Konstantinos Giannis, and Giuseppe F. Italiano

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

Abstract
Let G be a directed graph with n vertices and m edges. We present a deterministic algorithm that maintains the 2-edge-connected components of G under a sequence of m edge insertions, with a total running time of O(n² log n). This significantly improves upon the previous best bound of O(mn) for graphs that are not very sparse. After each insertion, our algorithm supports the following queries with asymptotically optimal efficiency: - Test in constant time whether two query vertices v and w are 2-edge-connected in G. - Report in O(n) time all the 2-edge-connected components of G. Our approach builds on the recent framework of Georgiadis, Italiano, and Kosinas [FOCS 2024] for computing the 3-edge-connected components of a directed graph in linear time, which leverages the minset-poset technique of Gabow [TALG 2016]. Additionally, we provide a deterministic decremental algorithm for maintaining 2-edge-connectivity in strongly connected directed graphs. Given a sequence of m edge deletions, our algorithm maintains the 2-edge-connected components in total time n^(2+o(1)), while supporting the same queries as the incremental algorithm. This result assumes that the edges of a fixed spanning tree of G and of its reverse graph G^R are not deleted. Previously, the best known bound for the decremental problem was O(mn log n), obtained by a randomized algorithm without restrictions on the deletions. In contrast to prior dynamic algorithms for 2-edge-connectivity in directed graphs, our method avoids the incremental computation of dominator trees, thereby circumventing the known conditional lower bound of Ω(mn).
Cite as

Loukas Georgiadis, Konstantinos Giannis, and Giuseppe F. Italiano. Faster Dynamic 2-Edge Connectivity in Directed Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{georgiadis_et_al:LIPIcs.ESA.2025.26,
  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Italiano, Giuseppe F.},
  title =	{{Faster Dynamic 2-Edge Connectivity in Directed Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{26:1--26:16},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-244945},
  doi =		{10.4230/LIPIcs.ESA.2025.26},
  annote =	{Keywords: Connectivity, dynamic algorithms, directed graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.19
On Finding 𝓁-Th Smallest Perfect Matchings

Authors: Nicolas El Maalouly, Sebastian Haslebacher, Adrian Taubner, and Lasse Wulf

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

Abstract
Given an undirected weighted graph G and an integer k, Exact-Weight Perfect Matching (EWPM) is the problem of finding a perfect matching of weight exactly k in G. In this paper, we study EWPM and its variants. The EWPM problem is famous, since in the case of unary encoded weights, Mulmuley, Vazirani, and Vazirani showed almost 40 years ago that the problem can be solved in randomized polynomial time. However, up to this date no derandomization is known. Our first result is a simple deterministic algorithm for EWPM that runs in time n^𝒪(𝓁), where 𝓁 is the number of distinct weights that perfect matchings in G can take. In fact, we show how to find an 𝓁-th smallest perfect matching in any weighted graph (even if the weights are encoded in binary, in which case EWPM in general is known to be NP-complete) in time n^𝒪(𝓁) for any integer 𝓁. Similar next-to-optimal variants have also been studied recently for the shortest path problem. For our second result, we extend the list of problems that are known to be equivalent to EWPM. We show that EWPM is equivalent under a weight-preserving reduction to the Exact Cycle Sum problem (ECS) in undirected graphs with a conservative (i.e. no negative cycles) weight function. To the best of our knowledge, we are the first to study this problem. As a consequence, the latter problem is contained in RP if the weights are encoded in unary. Finally, we identify a special case of EWPM, called BCPM, which was recently studied by El Maalouly, Steiner and Wulf. We show that BCPM is equivalent under a weight-preserving transformation to another problem recently studied by Schlotter and Sebő as well as Geelen and Kapadia: the Shortest Odd Cycle problem (SOC) in undirected graphs with conservative weights. Finally, our n^𝒪(𝓁) algorithm works in this setting as well, identifying a tractable special case of SOC, BCPM, and ECS.
Cite as

Nicolas El Maalouly, Sebastian Haslebacher, Adrian Taubner, and Lasse Wulf. On Finding 𝓁-Th Smallest Perfect Matchings. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elmaalouly_et_al:LIPIcs.ESA.2025.19,
  author =	{El Maalouly, Nicolas and Haslebacher, Sebastian and Taubner, Adrian and Wulf, Lasse},
  title =	{{On Finding 𝓁-Th Smallest Perfect Matchings}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{19:1--19:15},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-244875},
  doi =		{10.4230/LIPIcs.ESA.2025.19},
  annote =	{Keywords: Exact Matching, Perfect Matching, Exact-Weight Perfect Matching, Shortest Odd Cycle, Exact Cycle Sum, l-th Smallest Solution, l-th Largest Solution, k-th Best Solution, Derandomization}
}
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.2025.44
Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity

Authors: Koustav Bhanja and Asaf Petruschka

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

Abstract
We present a compact labeling scheme for determining whether a designated set of terminals in a graph remains connected after any f (or less) vertex failures occur. An f-FT Steiner connectivity labeling scheme for an n-vertex graph G = (V,E) with terminal set U ⊆ V provides labels to the vertices of G, such that given only the labels of any subset F ⊆ V with |F| ≤ f, one can determine if U remains connected in G-F. The main complexity measure is the maximum label length. The special case U = V of global connectivity has been recently studied by Jiang, Parter, and Petruschka [Yonggang Jiang et al., 2025], who provided labels of n^{1-1/f} ⋅ poly(f,log n) bits. This is near-optimal (up to poly(f,log n) factors) by a lower bound of Long, Pettie and Saranurak [Yaowei Long et al., 2025]. Our scheme achieves labels of |U|^{1-1/f} ⋅ poly(f, log n) for general U ⊆ V, which is near-optimal for any given size |U| of the terminal set. To handle terminal sets, our approach differs from [Yonggang Jiang et al., 2025]. We use a well-structured Steiner tree for U produced by a decomposition theorem of Duan and Pettie [Ran Duan and Seth Pettie, 2020], and bypass the need for Nagamochi-Ibaraki sparsification [Hiroshi Nagamochi and Toshihide Ibaraki, 1992].
Cite as

Koustav Bhanja and Asaf Petruschka. Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 44:1-44:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhanja_et_al:LIPIcs.ESA.2025.44,
  author =	{Bhanja, Koustav and Petruschka, Asaf},
  title =	{{Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{44:1--44:13},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-245123},
  doi =		{10.4230/LIPIcs.ESA.2025.44},
  annote =	{Keywords: Fault Tolerance, Labeling Schemes, Steiner Connectivity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.36
Efficient Contractions of Dynamic Graphs - With Applications

Authors: Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke

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

Abstract
A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors. We discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.
Cite as

Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke. Efficient Contractions of Dynamic Graphs - With Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.36,
  author =	{Henzinger, Monika and Kosinas, Evangelos and M\"{u}nk, Robin and R\"{a}cke, Harald},
  title =	{{Efficient Contractions of Dynamic Graphs - With Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{36:1--36:14},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-245047},
  doi =		{10.4230/LIPIcs.ESA.2025.36},
  annote =	{Keywords: Graph Algorithms, Cut Sparsifiers, Dynamic Algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.4
Streaming Algorithms for Network Design

Authors: Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph G = (V, E) and an integer connectivity requirement r(uv) for each u, v ∈ V. The objective is to find a minimum-weight subgraph H ⊆ G such that, for every pair of vertices u, v ∈ V, u and v are r(uv)-edge/vertex-connected. Recent work by [Ce Jin et al., 2024] obtained approximation algorithms for edge-connectivity augmentation, and via that, also derived algorithms for edge-connectivity SNDP (EC-SNDP). In this work we consider vertex-connectivity setting (VC-SNDP) and obtain several results for it as well as improved results for EC-SNDP. - We provide a general framework for solving connectivity problems including SNDP and others in streaming; this is based on a connection to fault-tolerant spanners. For VC-SNDP we provide an O(tk)-approximation in Õ(k^{1-1/t}n^{1 + 1/t}) space, where k is the maximum connectivity requirement, assuming an exact algorithm at the end of the stream. Using a refined LP-based analysis, we provide an O(β t)-approximation where β is the integrality gap of the natural cut-based LP relaxation. These are the first approximation algorithms in the streaming model for VC-SNDP. When applied to the EC-SNDP, our framework provides an O(t)-approximation in Õ(k^{1/2-1/(2t)}n^{1 + 1/t} + kn) space, improving the O(t log k)-approximation of [Ce Jin et al., 2024] using Õ(kn^{1+1/t}) space; this also extends to element-connectivity SNDP. - We consider vertex connectivity-augmentation in the link-arrival model. The input is a k-vertex-connected spanning subgraph G, and additional weighted links L arrive in the stream; the goal is to store the min-weight set of links such that G ∪ L is (k+1)-vertex-connected. We obtain constant-factor approximations in near-linear space for k = 1, 2. Our result for k = 2 is based on using the SPQR tree, a novel application for this well-known representation of 2-connected graphs.
Cite as

Chandra Chekuri, Rhea Jain, Sepideh Mahabadi, and Ali Vakilian. Streaming Algorithms for Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 4:1-4:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2025.4,
  author =	{Chekuri, Chandra and Jain, Rhea and Mahabadi, Sepideh and Vakilian, Ali},
  title =	{{Streaming Algorithms for Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{4:1--4:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  URN =		{urn:nbn:de:0030-drops-243709},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.4},
  annote =	{Keywords: Streaming Algorithms, Survivable Network Design, Fault-Tolerant Spanners}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.18
A Randomized Rounding Approach for DAG Edge Deletion

Authors: Sina Kalantarzadeh, Nathan Klein, and Victor Reis

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
In the DAG Edge Deletion problem, we are given an edge-weighted directed acyclic graph and a parameter k, and the goal is to delete the minimum weight set of edges so that the resulting graph has no paths of length k. This problem, which has applications to scheduling, was introduced in 2015 by Kenkre, Pandit, Purohit, and Saket. They gave a k-approximation and showed that it is UGC-Hard to approximate better than ⌊0.5k⌋ for any constant k ≥ 4 using a work of Svensson from 2012. The approximation ratio was improved to 2/3(k+1) by Klein and Wexler in 2016. In this work, we introduce a randomized rounding framework based on distributions over vertex labels in [0,1]. The most natural distribution is to sample labels independently from the uniform distribution over [0,1]. We show this leads to a (2-√2)(k+1) ≈ 0.585(k+1)-approximation. By using a modified (but still independent) label distribution, we obtain a 0.549(k+1)-approximation for the problem, as well as show that no independent distribution over labels can improve our analysis to below 0.542(k+1). Finally, we show a 0.5(k+1)-approximation for bipartite graphs and for instances with structured LP solutions. Whether this ratio can be obtained in general is open.
Cite as

Sina Kalantarzadeh, Nathan Klein, and Victor Reis. A Randomized Rounding Approach for DAG Edge Deletion. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 18:1-18:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kalantarzadeh_et_al:LIPIcs.APPROX/RANDOM.2025.18,
  author =	{Kalantarzadeh, Sina and Klein, Nathan and Reis, Victor},
  title =	{{A Randomized Rounding Approach for DAG Edge Deletion}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{18:1--18:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  URN =		{urn:nbn:de:0030-drops-243840},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.18},
  annote =	{Keywords: Approximation Algorithms, Randomized Algorithms, Linear Programming, Graph Algorithms, Scheduling}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.5
On Planar Straight-Line Dominance Drawings

Authors: Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali

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

Abstract
We study the following question, which has been considered since the 90’s: Does every st-planar graph admit a planar straight-line dominance drawing? We show concrete evidence for the difficulty of this question, by proving that, unlike upward planar straight-line drawings, planar straight-line dominance drawings with prescribed y-coordinates do not always exist and planar straight-line dominance drawings cannot always be constructed via a contract-draw-expand inductive approach. We also show several classes of st-planar graphs that always admit a planar straight-line dominance drawing. These include st-planar 3-trees in which every stacking operation introduces two edges incoming into the new vertex, st-planar graphs in which every vertex is adjacent to the sink, and st-planar graphs in which no face has the left boundary that is a single edge.
Cite as

Patrizio Angelini, Michael A. Bekos, Giuseppe Di Battista, Fabrizio Frati, Luca Grilli, and Giacomo Ortali. On Planar Straight-Line Dominance Drawings. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{angelini_et_al:LIPIcs.WADS.2025.5,
  author =	{Angelini, Patrizio and Bekos, Michael A. and Di Battista, Giuseppe and Frati, Fabrizio and Grilli, Luca and Ortali, Giacomo},
  title =	{{On Planar Straight-Line Dominance Drawings}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{5:1--5:18},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-242361},
  doi =		{10.4230/LIPIcs.WADS.2025.5},
  annote =	{Keywords: st-graphs, dominance drawings, planar straight-line drawings, upward planarity}
}
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