108 Search Results for "Mathieu, Claire"

Volume

LIPIcs, Volume 60

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

APPROX/RANDOM 2016, September 7-9, 2016, Paris, France

Editors: Klaus Jansen, Claire Mathieu, José D. P. Rolim, and Chris Umans

Document
DOI: 10.4230/DagRep.15.3.94
Scheduling (Dagstuhl Seminar 25121)

Authors: Claire Mathieu, Nicole Megow, Benjamin J. Moseley, Frits C. R. Spieksma, and Alexander Lindermayr

Published in: Dagstuhl Reports, Volume 15, Issue 3 (2025)

Abstract
This report documents the program and outcomes of Dagstuhl Seminar 25121, "Scheduling". The seminar focused on bridging traditional algorithmic scheduling with the emerging field of fairness in resource allocation. Scheduling is a longstanding research area that has been studied from both practical and theoretical perspectives in computer science, mathematical optimization, and operations research for over 70 years. Fairness has become a key concern in recent years, particularly in the context of resource allocation and scheduling, where it naturally arises in applications such as kidney exchange, school choice, and political districting. The seminar centered on three main themes: (1) fair allocation, (2) fairness versus quality of service, and (3) modeling aspects of fairness in scheduling.
Cite as

Claire Mathieu, Nicole Megow, Benjamin J. Moseley, Frits C. R. Spieksma, and Alexander Lindermayr. Scheduling (Dagstuhl Seminar 25121). In Dagstuhl Reports, Volume 15, Issue 3, pp. 94-112, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{mathieu_et_al:DagRep.15.3.94,
  author =	{Mathieu, Claire and Megow, Nicole and Moseley, Benjamin J. and Spieksma, Frits C. R. and Lindermayr, Alexander},
  title =	{{Scheduling (Dagstuhl Seminar 25121)}},
  pages =	{94--112},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2025},
  volume =	{15},
  number =	{3},
  editor =	{Mathieu, Claire and Megow, Nicole and Moseley, Benjamin J. and Spieksma, Frits C. R. and Lindermayr, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.15.3.94},
  URN =		{urn:nbn:de:0030-drops-248981},
  doi =		{10.4230/DagRep.15.3.94},
  annote =	{Keywords: scheduling, fairness, mathematical optimization, algorithms and complexity, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.74
Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications

Authors: Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka

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

Abstract
Min-plus matrix multiplication is a fundamental tool for designing algorithms operating on distances in graphs and different problems solvable by dynamic programming. We know that, assuming the APSP hypothesis, no subcubic-time algorithm exists for the case of general matrices. However, in many applications the matrices admit certain structural properties that can be used to design faster algorithms. For example, when considering a planar graph, one often works with a Monge matrix A, meaning that the density matrix A^◻ has non-negative entries, that is, A^◻_{i,j} := A_{i+1,j} + A_{i,j+1} - A_{i,j} -A_{i+1,j+1} ≥ 0. The min-plus product of two n×n Monge matrices can be computed in 𝒪(n²) time using the famous SMAWK algorithm. In applications such as longest common subsequence, edit distance, and longest increasing subsequence, the matrices are even more structured, as observed by Tiskin [J. Discrete Algorithms, 2008]: they are (or can be converted to) simple unit-Monge matrices, meaning that the density matrix is a permutation matrix and, furthermore, the first column and the last row of the matrix consist of only zeroes. Such matrices admit an implicit representation of size 𝒪(n) and, as shown by Tiskin [SODA 2010 & Algorithmica, 2015], their min-plus product can be computed in 𝒪(nlog n) time. Russo [SPIRE 2010 & Theor. Comput. Sci., 2012] identified a general structural property of matrices that admit such efficient representation and min-plus multiplication algorithms: the core size δ, defined as the number of non-zero entries in the density matrices of the input and output matrices. He provided an adaptive implementation of the SMAWK algorithm that runs in 𝒪((n+δ)log³ n) or 𝒪((n+δ)log² n) time (depending on the representation of the input matrices). In this work, we further investigate the core size as the parameter that enables efficient min-plus matrix multiplication. On the combinatorial side, we provide a (linear) bound on the core size of the product matrix in terms of the core sizes of the input matrices. On the algorithmic side, we generalize Tiskin’s algorithm (but, arguably, with a more elementary analysis) to solve the core-sparse Monge matrix multiplication problem in 𝒪(n+δlog δ) ⊆ 𝒪(n + δ log n) time, matching the complexity for simple unit-Monge matrices. As witnessed by the recent work of Gorbachev and Kociumaka [STOC'25] for edit distance with integer weights, our generalization opens up the possibility of speed-ups for weighted sequence alignment problems. Furthermore, our multiplication algorithm is also capable of producing an efficient data structure for recovering the witness for any given entry of the output matrix. This allows us, for example, to preprocess an integer array of size n in Õ(n) time so that the longest increasing subsequence of any sub-array can be reconstructed in Õ(𝓁) time, where 𝓁 is the length of the reported subsequence. In comparison, Karthik C. S. and Rahul [arXiv, 2024] recently achieved 𝒪(𝓁+n^{1/2}polylog n)-time reporting after 𝒪(n^{3/2}polylog n)-time preprocessing.
Cite as

Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka. Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.74,
  author =	{Gawrychowski, Pawe{\l} and Gorbachev, Egor and Kociumaka, Tomasz},
  title =	{{Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{74:1--74:17},
  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.2025.74},
  URN =		{urn:nbn:de:0030-drops-245427},
  doi =		{10.4230/LIPIcs.ESA.2025.74},
  annote =	{Keywords: Min-plus matrix multiplication, Monge matrix, longest increasing subsequence}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.69
Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing

Authors: David Eppstein, Michael T. Goodrich, and Songyu (Alfred) Liu

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

Abstract
We provide the first approximation quality guarantees for the Cuthull-McKee heuristic for reordering symmetric matrices to have low bandwidth, and we provide an algorithm for reconstructing bounded-bandwidth graphs from distance oracles with near-linear query complexity. To prove these results we introduce a new width parameter, BFS width, and we prove polylogarithmic upper and lower bounds on the BFS width of graphs of bounded bandwidth. Unlike other width parameters, such as bandwidth, pathwidth, and treewidth, BFS width can easily be computed in polynomial time. Bounded BFS width implies bounded bandwidth, pathwidth, and treewidth, which in turn imply fixed-parameter tractable algorithms for many problems that are NP-hard for general graphs. In addition to their applications to matrix ordering, we also provide applications of BFS width to graph reconstruction, to reconstruct graphs from distance queries, and graph drawing, to construct arc diagrams of small height.
Cite as

David Eppstein, Michael T. Goodrich, and Songyu (Alfred) Liu. Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 69:1-69:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein_et_al:LIPIcs.ESA.2025.69,
  author =	{Eppstein, David and Goodrich, Michael T. and Liu, Songyu (Alfred)},
  title =	{{Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{69:1--69:17},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-245373},
  doi =		{10.4230/LIPIcs.ESA.2025.69},
  annote =	{Keywords: Graph algorithms, graph theory, graph width, bandwidth, treewidth}
}
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.2025.111
Hardness of Median and Center in the Ulam Metric

Authors: Nick Fischer, Elazar Goldenberg, Mursalin Habib, and Karthik C. S.

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

Abstract
The classical rank aggregation problem seeks to combine a set X of n permutations into a single representative "consensus" permutation. In this paper, we investigate two fundamental rank aggregation tasks under the well-studied Ulam metric: computing a median permutation (which minimizes the sum of Ulam distances to X) and computing a center permutation (which minimizes the maximum Ulam distance to X) in two settings. - Continuous Setting: In the continuous setting, the median/center is allowed to be any permutation. It is known that computing a center in the Ulam metric is NP-hard and we add to this by showing that computing a median is NP-hard as well via a simple reduction from the Max-Cut problem. While this result may not be unexpected, it had remained elusive until now and confirms a speculation by Chakraborty, Das, and Krauthgamer [SODA '21]. - Discrete Setting: In the discrete setting, the median/center must be a permutation from the input set. We fully resolve the fine-grained complexity of the discrete median and discrete center problems under the Ulam metric, proving that the naive Õ(n² L)-time algorithm (where L is the length of the permutation) is conditionally optimal. This resolves an open problem raised by Abboud, Bateni, Cohen-Addad, Karthik C. S., and Seddighin [APPROX '23]. Our reductions are inspired by the known fine-grained lower bounds for similarity measures, but we face and overcome several new highly technical challenges.
Cite as

Nick Fischer, Elazar Goldenberg, Mursalin Habib, and Karthik C. S.. Hardness of Median and Center in the Ulam Metric. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 111:1-111:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ESA.2025.111,
  author =	{Fischer, Nick and Goldenberg, Elazar and Habib, Mursalin and Karthik C. S.},
  title =	{{Hardness of Median and Center in the Ulam Metric}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{111:1--111:17},
  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.2025.111},
  URN =		{urn:nbn:de:0030-drops-245809},
  doi =		{10.4230/LIPIcs.ESA.2025.111},
  annote =	{Keywords: Ulam distance, median, center, rank aggregation, fine-grained complexity}
}
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.2025.27
Triangles Improve 0.878 Approximation for Maxcut

Authors: Fredie George, Anand Louis, and Rameesh Paul

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

Abstract
Maxcut is a fundamental problem in graph algorithms, extensively studied for its theoretical and practical significance. The goal is to partition the vertex set of a graph G = (V, E) into disjoint subsets S and V⧵S so as to maximize the number of edges crossing the cut (S,V⧵S). The seminal work of Goemans and Williamson [Goemans and Williamson, 1995] introduced a semidefinite programming (SDP) based algorithm achieving a α_{GW} ≈ 0.87856-approximation for general graphs, guaranteed to be optimal under the Unique Games Conjecture [Khot, 2002; Khot et al., 2007]. We revisit the Goemans–Williamson SDP and prove that the standard Maxcut SDP achieves a (α_{GW} + Ω(1))-approximation whenever the input graph contains Ω(|E|) edge-disjoint triangles. Our analysis builds on classical rounding techniques studied in [Goemans and Williamson, 1995; Zwick, 1999] and introduces a refined understanding of the SDP solution structure in regimes where the previous guarantees are tight. Our result identifies a simple combinatorial property that may be satisfied by many natural graph classes. As applications, we show that unit ball graphs and graphs satisfying a spectral transitivity condition (as studied in [Gupta et al., 2016; Basu et al., 2024]) meet our structural criterion, and therefore we get better than α_{GW} approximation guarantees for them. Our algorithm runs in nearly linear time 𝒪̃(|E|), offering a more practical alternative to the PTAS of [Jansen et al., 2005] for unit ball graphs, which has exponential dependence on the approximation parameter.
Cite as

Fredie George, Anand Louis, and Rameesh Paul. Triangles Improve 0.878 Approximation for Maxcut. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 27:1-27:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{george_et_al:LIPIcs.APPROX/RANDOM.2025.27,
  author =	{George, Fredie and Louis, Anand and Paul, Rameesh},
  title =	{{Triangles Improve 0.878 Approximation for Maxcut}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{27:1--27:25},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-243931},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.27},
  annote =	{Keywords: Approximation Algorithms, Maxcut, Semidefinite Programming, Edge-disjoint Triangles, Unit Ball Graphs, Spectral Triadic Graphs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.5
Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT

Authors: Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma

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

Abstract
This paper studies complete k-Constraint Satisfaction Problems (CSPs), where an n-variable instance has exactly one nontrivial constraint for each subset of k variables, i.e., it has binom(n,k) constraints. A recent work started a systematic study of complete k-CSPs [Anand, Lee, Sharma, SODA'25], and showed a quasi-polynomial time algorithm that decides if there is an assignment satisfying all the constraints of any complete Boolean-alphabet k-CSP, algorithmically separating complete instances from dense instances. The tractability of this decision problem is necessary for any nontrivial (multiplicative) approximation for the minimization version, whose goal is to minimize the number of violated constraints. The same paper raised the question of whether it is possible to obtain nontrivial approximation algorithms for complete Min-k-CSPs with k ≥ 3. In this work, we make progress in this direction and show a quasi-polynomial time polylog(n)-approximation to Min-NAE-3-SAT on complete instances, which asks to minimize the number of 3-clauses where all the three literals equal the same bit. To the best of our knowledge, this is the first known example of a CSP whose decision version is NP-Hard in general (and dense) instances while admitting a polylog(n)-approximation in complete instances. Our algorithm presents a new iterative framework for rounding a solution from the Sherali-Adams hierarchy, where each iteration interleaves the two well-known rounding tools: the conditioning procedure, in order to "almost fix" many variables, and the thresholding procedure, in order to "completely fix" them. Finally, we improve the running time of the decision algorithms of Anand, Lee, and Sharma and show a simple algorithm that decides any complete Boolean-alphabet k-CSP in polynomial time.
Cite as

Aditya Anand, Euiwoong Lee, Davide Mazzali, and Amatya Sharma. Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{anand_et_al:LIPIcs.APPROX/RANDOM.2025.5,
  author =	{Anand, Aditya and Lee, Euiwoong and Mazzali, Davide and Sharma, Amatya},
  title =	{{Min-CSPs on Complete Instances II: Polylogarithmic Approximation for Min-NAE-3-SAT}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{5:1--5:23},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-243712},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.5},
  annote =	{Keywords: Constraint Satisfiability Problems, Approximation Algorithms, Sherali Adams}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.20
Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson

Authors: Jungho Ahn, Ian DeHaan, Eun Jung Kim, and Euiwoong Lee

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

Abstract
We present a polynomial-time (α_{GW} + ε)-approximation algorithm for the Maximum Cut problem on interval graphs and split graphs, where α_{GW} ≈ 0.878 is the approximation guarantee of the Goemans-Williamson algorithm and ε > 10^{-34} is a fixed constant. To attain this, we give an improved analysis of a slight modification of the Goemans-Williamson algorithm for graphs in which triangles can be packed into a constant fraction of their edges. We then pair this analysis with structural results showing that both interval graphs and split graphs either have such a triangle packing or have maximum cut close to their number of edges. We also show that, subject to the Small Set Expansion Hypothesis, there exists a constant c > 0 such that there is no polyomial-time (1 - c)-approximation for Maximum Cut on split graphs.
Cite as

Jungho Ahn, Ian DeHaan, Eun Jung Kim, and Euiwoong Lee. Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ahn_et_al:LIPIcs.APPROX/RANDOM.2025.20,
  author =	{Ahn, Jungho and DeHaan, Ian and Kim, Eun Jung and Lee, Euiwoong},
  title =	{{Approximating Maximum Cut on Interval Graphs and Split Graphs Beyond Goemans-Williamson}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{20:1--20:22},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-243869},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.20},
  annote =	{Keywords: Maximum cut, graph theory, interval graphs, split graphs}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.50
Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries

Authors: Tatsuya Terao

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

Abstract
In the matroid intersection problem, we are given two matroids ℳ₁ = (V, ℐ₁) and ℳ₂ = (V, ℐ₂) defined on the same ground set V of n elements, and the objective is to find a common independent set S ∈ ℐ₁ ∩ ℐ₂ of largest possible cardinality, denoted by r. In this paper, we consider a deterministic matroid intersection algorithm with only a nearly linear number of independence oracle queries. Our contribution is to present a deterministic O(n/(ε) + r log r)-independence-query (2/3-ε)-approximation algorithm for any ε > 0. Our idea is very simple: we apply a recent Õ(n √r/ε)-independence-query (1 - ε)-approximation algorithm of Blikstad [ICALP 2021], but terminate it before completion. Moreover, we also present a semi-streaming algorithm for (2/3 -ε)-approximation of matroid intersection in O(1/ε) passes.
Cite as

Tatsuya Terao. Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{terao:LIPIcs.WADS.2025.50,
  author =	{Terao, Tatsuya},
  title =	{{Deterministic (2/3 - \epsilon)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{50:1--50:18},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-242812},
  doi =		{10.4230/LIPIcs.WADS.2025.50},
  annote =	{Keywords: Matroid intersection, approximation algorithm, streaming algorithm}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.24
Computational Geometry with Probabilistically Noisy Primitive Operations

Authors: David Eppstein, Michael T. Goodrich, and Vinesh Sridhar

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

Abstract
Much prior work has been done on designing computational geometry algorithms that handle input degeneracies, data imprecision, and arithmetic round-off errors. We take a new approach, inspired by the noisy sorting literature, and study computational geometry algorithms subject to noisy Boolean primitive operations in which, e.g., the comparison "is point q above line 𝓁?" returns the wrong answer with some fixed probability. We propose a novel technique called path-guided pushdown random walks that generalizes the results of noisy sorting. We apply this technique to solve point-location, plane-sweep, convex hulls in 2D and 3D, and Delaunay triangulations for noisy primitives in optimal time with high probability.
Cite as

David Eppstein, Michael T. Goodrich, and Vinesh Sridhar. Computational Geometry with Probabilistically Noisy Primitive Operations. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein_et_al:LIPIcs.WADS.2025.24,
  author =	{Eppstein, David and Goodrich, Michael T. and Sridhar, Vinesh},
  title =	{{Computational Geometry with Probabilistically Noisy Primitive Operations}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{24:1--24:20},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-242552},
  doi =		{10.4230/LIPIcs.WADS.2025.24},
  annote =	{Keywords: Computational geometry, noisy comparisons, random walks}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.27
A QPTAS for Facility Location on Unit Disk Graphs

Authors: Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun

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

Abstract
We study the classic (Uncapacitated) Facility Location problem on Unit Disk Graphs (UDGs). For a given point set P in the plane, the unit disk graph UDG(P) on P has vertex set P and an edge between two distinct points p, q ∈ P if and only if their Euclidean distance |pq| is at most 1. The weight of the edge pq is equal to their distance |pq|. An instance of {Facility Location} on UDG(P) consists of a set C ⊆ P of clients and a set F ⊆ P of facilities, each having an opening cost f_i. The goal is to pick a subset F' ⊆ F to open while minimizing ∑_{i ∈ F'} f_i + ∑_{v ∈ C} d(v,F'), where d(v,F') is the distance of v to nearest facility in F' through UDG(P). In this paper, we present the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem. While approximation schemes are well-established for facility location problems on sparse geometric graphs (such as planar graphs), there is a lack of such results for dense graphs. Specifically, prior to this study, to the best of our knowledge, there was no approximation scheme for any facility location problem on UDGs in the general setting.
Cite as

Zachary Friggstad, Mohsen Rezapour, Mohammad R. Salavatipour, and Hao Sun. A QPTAS for Facility Location on Unit Disk Graphs. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friggstad_et_al:LIPIcs.WADS.2025.27,
  author =	{Friggstad, Zachary and Rezapour, Mohsen and Salavatipour, Mohammad R. and Sun, Hao},
  title =	{{A QPTAS for Facility Location on Unit Disk Graphs}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{27:1--27:18},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-242586},
  doi =		{10.4230/LIPIcs.WADS.2025.27},
  annote =	{Keywords: Facility Location, Unit Disk Graphs, Approximation Algorithms}
}
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.CCC.2025.2
Hardness Amplification for Real-Valued Functions

Authors: Yunqi Li and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Given an integer-valued function f:{0,1}ⁿ → {0,1,… , m-1} that is mildly hard to compute on instances drawn from some distribution D over {0,1}ⁿ, we show that the function g(x_1, … , x_t) = f(x_1) + ⋯ + f(x_t) is strongly hard to compute on instances (x_1,… ,x_t) drawn from the product distribution D^t. We also show the same for the task of approximately computing real-valued functions f:{0,1}ⁿ → [0,m). Our theorems immediately imply hardness self-amplification for several natural problems including Max-Clique and Max-SAT, Approximate #SAT, Entropy Estimation, etc..
Cite as

Yunqi Li and Prashant Nalini Vasudevan. Hardness Amplification for Real-Valued Functions. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 2:1-2:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.CCC.2025.2,
  author =	{Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Hardness Amplification for Real-Valued Functions}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{2:1--2:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.2},
  URN =		{urn:nbn:de:0030-drops-236967},
  doi =		{10.4230/LIPIcs.CCC.2025.2},
  annote =	{Keywords: Average-case complexity, hardness amplification}
}
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