30 Search Results for "Goranci, Gramoz"

Document
DOI: 10.4230/LIPIcs.STACS.2026.38
Fully Dynamic Spectral Sparsification for Directed Hypergraphs

Authors: Sebastian Forster, Gramoz Goranci, and Ali Momeni

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

Abstract
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph sparsifiers of directed hypergraphs. Our algorithm achieves a near-optimal size of O(n² / ε ² log ⁷ m) and amortized update time of O(r² log ³ m), where n is the number of vertices, and m and r respectively upper bound the number of hyperedges and the rank of the hypergraph at any time. We also extend our approach to the parallel batch-dynamic setting, where a batch of any k hyperedge insertions or deletions can be processed with O(kr² log ³ m) amortized work and O(log ² m) depth. This constitutes the first spectral-based sparsification algorithm in this setting.
Cite as

Sebastian Forster, Gramoz Goranci, and Ali Momeni. Fully Dynamic Spectral Sparsification for Directed Hypergraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{forster_et_al:LIPIcs.STACS.2026.38,
  author =	{Forster, Sebastian and Goranci, Gramoz and Momeni, Ali},
  title =	{{Fully Dynamic Spectral Sparsification for Directed Hypergraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{38:1--38:20},
  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.2026.38},
  URN =		{urn:nbn:de:0030-drops-255272},
  doi =		{10.4230/LIPIcs.STACS.2026.38},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.69
Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time

Authors: Etienne Objois and Adrian Vladu

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

Abstract
We provide the first nearly-linear time algorithm for approximating 𝓁_{q → p}-norms of non-negative matrices, for q ≥ p ≥ 1. Our algorithm returns a (1-ε)-approximation to the matrix norm in time Õ(1/(q ε) ⋅ nnz(A)), where A is the input matrix, and improves upon the previous state of the art, which either proved convergence only in the limit [Boyd '74], or had very high polynomial running times [Bhaskara-Vijayraghavan, SODA '11]. Our algorithm is extremely simple, and is largely inspired from the coordinate-scaling approach used for positive linear program solvers. Our algorithm can readily be used in the [Englert-Räcke, FOCS '09] to improve the running time of constructing O(log n)-competitive 𝓁_p-oblivious routings.
Cite as

Etienne Objois and Adrian Vladu. Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 69:1-69:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{objois_et_al:LIPIcs.STACS.2026.69,
  author =	{Objois, Etienne and Vladu, Adrian},
  title =	{{Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{69:1--69:19},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-255585},
  doi =		{10.4230/LIPIcs.STACS.2026.69},
  annote =	{Keywords: matrix norm, Perron-Frobenius theory, oblivious routings, input-sparsity time, lp norm}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.5
Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs

Authors: Mridul Ahi, Keerti Choudhary, Shlok Pande, Pushpraj, and Lakshay Saggi

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

Abstract
This paper addresses the problem of designing fault-tolerant data structures for the (s,t)-max-flow and (s,t)-min-cut problems in unweighted directed graphs. Given a directed graph G = (V, E) with a designated source s, sink t, and an (s,t)-max-flow of value λ, we present constructions for max-flow and min-cut sensitivity oracles, and introduce the concept of a fault-tolerant flow family, which may be of independent interest. Our main contributions are as follows. 1) Fault-Tolerant Flow Family: We construct a family ℬ of 2λ+1 (s,t)-flows such that for every edge e, ℬ contains an (s,t)-max-flow of G-e. This covering property is tight up to constants for single failures and provably cannot extend to comparably small families for k ≥ 2, where we show an Ω(n) lower bound on the family size, independent of λ. 2) Max-Flow Sensitivity Oracle: Using the fault-tolerant flow family, we construct a single as well as dual-edge sensitivity oracle for (s,t)-max-flow that requires only O(λ n) space. Given any set F of up to two failing edges, the oracle reports the updated max-flow value in G-F in O(n) time. Additionally, for the single-failure case, the oracle can determine in constant time whether the flow through an edge x changes when another edge e fails. 3) Min-Cut Sensitivity Oracle for Dual Failures: Recently, Baswana et al. (ICALP’22) designed an O(n²)-sized oracle for answering (s,t)-min-cut size queries under dual edge failures in constant time, along with a matching lower bound. We extend this by focusing on graphs with small min-cut values λ, and present a more compact oracle of size O(λ n) that answers such min-cut size queries in constant time and reports the corresponding (s,t)-min-cut partition in O(n) time. We also show that the space complexity of our oracle is asymptotically optimal in this setting. 4) Min-Cut Sensitivity Oracle for Multiple Failures: We extend our results to the general case of k edge failures. For any graph with (s,t)-min-cut of size λ, we construct a k-fault-tolerant min-cut oracle with space complexity O_{λ,k}(n log n) that answers min-cut size queries in O_{λ,k}(log n) time. This also leads to improved fault-tolerant (s,t)-reachability oracles, achieving O(n log n) space and O(log n) query time for up to k = O(1) edge failures.
Cite as

Mridul Ahi, Keerti Choudhary, Shlok Pande, Pushpraj, and Lakshay Saggi. Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ahi_et_al:LIPIcs.ITCS.2026.5,
  author =	{Ahi, Mridul and Choudhary, Keerti and Pande, Shlok and Pushpraj and Saggi, Lakshay},
  title =	{{Maximum-Flow and Minimum-Cut Sensitivity Oracles for Directed Graphs}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{5:1--5:24},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-252920},
  doi =		{10.4230/LIPIcs.ITCS.2026.5},
  annote =	{Keywords: Fault tolerance, Data structures, Minimum cuts, Maximum flows}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.89
On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time

Authors: Tsz Chiu Kwok, Zhewei Wei, and Mingji Yang

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

Abstract
We initiate a study of solving a row/column diagonally dominant (RDD/CDD) linear system 𝐌x = b in sublinear time, with the goal of estimating t^{⊤}x^{∗} for a given vector t ∈ ℝⁿ and a specific solution x^{∗}. This setting naturally generalizes the study of sublinear-time solvers for symmetric diagonally dominant (SDD) systems [Andoni-Krauthgamer-Pogrow, ITCS 2019] to the asymmetric case, which has remained underexplored despite extensive work on nearly-linear-time solvers for RDD/CDD systems. Our first contributions are characterizations of the problem’s mathematical structure. We express a solution x^{∗} via a Neumann series, prove its convergence, and upper bound the truncation error on this series through a novel quantity of 𝐌, termed the maximum p-norm gap. This quantity generalizes the spectral gap of symmetric matrices and captures how the structure of 𝐌 governs the problem’s computational difficulty. For systems with bounded maximum p-norm gap, we develop a collection of algorithmic results for locally approximating t^{⊤}x^{∗} under various scenarios and error measures. We derive these results by adapting the techniques of random-walk sampling, local push, and their bidirectional combination, which have proved powerful for special cases of solving RDD/CDD systems, particularly estimating PageRank and effective resistance on graphs. Our general framework yields deeper insights, extended results, and improved complexity bounds for these problems. Notably, our perspective provides a unified understanding of Forward Push and Backward Push, two fundamental approaches for estimating random-walk probabilities on graphs. Our framework also inherits the hardness results for sublinear-time SDD solvers and local PageRank computation, establishing lower bounds on the maximum p-norm gap or the accuracy parameter. We hope that our work opens the door for further study into sublinear solvers, local graph algorithms, and directed spectral graph theory.
Cite as

Tsz Chiu Kwok, Zhewei Wei, and Mingji Yang. On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 89:1-89:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kwok_et_al:LIPIcs.ITCS.2026.89,
  author =	{Kwok, Tsz Chiu and Wei, Zhewei and Yang, Mingji},
  title =	{{On Solving Asymmetric Diagonally Dominant Linear Systems in Sublinear Time}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{89:1--89:25},
  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.2026.89},
  URN =		{urn:nbn:de:0030-drops-253768},
  doi =		{10.4230/LIPIcs.ITCS.2026.89},
  annote =	{Keywords: Spectral Graph Theory, Linear Systems, Sublinear Algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.25
Model-Agnostic Approximation of Constrained Forest Problems

Authors: Corinna Coupette, Alipasha Montaseri, and Christoph Lenzen

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

Abstract
Constrained Forest Problems (CFPs) as introduced by Goemans and Williamson in 1995 capture a wide range of network design problems with edge subsets as solutions, such as Minimum Spanning Tree, Steiner Forest, and Point-to-Point Connection. While individual CFPs have been studied extensively in individual computational models, a unified approach to solving general CFPs in multiple computational models has been lacking. Against this background, we present the shell-decomposition algorithm, a model-agnostic meta-algorithm that efficiently computes a (2+ε)-approximation to CFPs for a broad class of forest functions. The shell-decomposition algorithm isolates the problem-specific hardness of individual CFPs in a single computational subroutine, breaking the remainder of the computation into fundamental tasks that are studied extensively in a wide range of computational models. In contrast to prior work, our framework is compatible with the use of approximate distances. To demonstrate the power and flexibility of this result, we instantiate our algorithm for three fundamental, NP-hard CFPs (Steiner Forest, Point-to-Point Connection, and Facility Placement and Connection) in three different computational models (Congest, PRAM, and Multi-Pass Streaming). For constant ε, we obtain the following (2+ε)-approximations in the Congest model: [(1)] 1) For Steiner Forest specified via input components (SF-IC), where each node knows the identifier of one of k disjoint subsets of V (the input components), we achieve a deterministic (2+ε)-approximation in 𝒪̃(√n+D+k) rounds, where D is the hop diameter of the graph, significantly improving over the state of the art. 2) For Steiner Forest specified via symmetric connection requests (SF-SCR), where connection requests are issued to pairs of nodes u,v ∈ V, we leverage randomized equality testing to reduce the running time to 𝒪̃(√n+D), succeeding with high probability. 3) For Point-to-Point Connection, we provide a (2+ε)-approximation in 𝒪̃(√n+D) rounds. 4) For Facility Placement and Connection, a relative of non-metric Uncapacitated Facility Location, we obtain a (2+ε)-approximation in 𝒪̃(√n + D) rounds. We further show how to replace the √n+D term by the complexity of solving Partwise Aggregation, achieving (near-)universal optimality in any setting in which a solution to Partwise Aggregation in near-shortcut-quality time is known. Notably, all of our concrete results can be derived with relative ease once our model-agnostic meta-algorithm has been specified. This demonstrates the power of our modularization approach to algorithm design.
Cite as

Corinna Coupette, Alipasha Montaseri, and Christoph Lenzen. Model-Agnostic Approximation of Constrained Forest Problems. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 25:1-25:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coupette_et_al:LIPIcs.DISC.2025.25,
  author =	{Coupette, Corinna and Montaseri, Alipasha and Lenzen, Christoph},
  title =	{{Model-Agnostic Approximation of Constrained Forest Problems}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{25:1--25:24},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-248420},
  doi =		{10.4230/LIPIcs.DISC.2025.25},
  annote =	{Keywords: Distributed Graph Algorithms, Model-Agnostic Algorithms, Steiner Forest}
}
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.2025.107
Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts

Authors: Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang

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

Abstract
We show the existence of length-constrained expander decomposition in directed graphs and undirected vertex-capacitated graphs. Previously, its existence was shown only in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2022; Haeupler et al., 2024]. Along the way, we prove the multi-commodity maxflow-mincut theorems for length-constrained expansion in both directed and undirected vertex-capacitated graphs. Based on our decomposition, we build a length-constrained flow shortcut for undirected vertex-capacitated graphs, which roughly speaking is a set of edges and vertices added to the graph so that every multi-commodity flow demand can be routed with approximately the same vertex-congestion and length, but all flow paths only contain few edges. This generalizes the shortcut for undirected edge-capacitated graphs from [Bernhard Haeupler et al., 2024]. Length-constrained expander decomposition and flow shortcuts have been crucial in the recent algorithms in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2024; Haeupler et al., 2024]. Our work thus serves as a foundation to generalize these concepts to directed and vertex-capacitated graphs.
Cite as

Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang. Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 107:1-107:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haeupler_et_al:LIPIcs.ESA.2025.107,
  author =	{Haeupler, Bernhard and Long, Yaowei and Saranurak, Thatchaphol and Wang, Shengzhe},
  title =	{{Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{107:1--107:17},
  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.2025.107},
  URN =		{urn:nbn:de:0030-drops-245765},
  doi =		{10.4230/LIPIcs.ESA.2025.107},
  annote =	{Keywords: Length-Constrained Expander, Expander Decomposition, Shortcut}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.113
Bootstrapping Dynamic APSP via Sparsification

Authors: Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein

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

Abstract
We give a simple algorithm for the dynamic approximate All-Pairs Shortest Paths (APSP) problem. Given a graph G = (V, E, l) with polynomially bounded edge lengths, our data structure processes |E| edge insertions and deletions in total time |E|^{1+o(1)} and provides query access to |E|^o(1)-approximate distances in time Õ(1) per query. We produce a data structure that mimics Thorup-Zwick distance oracles [Thorup and Zwick, 2005], but is dynamic and deterministic. Our algorithm selects a small number of pivot vertices. Then, for every other vertex, it reduces distance computation to maintaining distances to a small neighborhood around that vertex and to the nearest pivot. We maintain distances between pivots efficiently by representing them in a smaller graph and recursing. We maintain these smaller graphs by (a) reducing vertex count using the dynamic distance-preserving core graphs of Kyng-Meierhans-Probst Gutenberg [Kyng et al., 2024] in a black-box manner and (b) reducing edge-count using a dynamic spanner akin to Chen-Kyng-Liu-Meierhans-Probst Gutenberg [Chen et al., 2024]. Our dynamic spanner internally uses an APSP data structure. Choosing a large enough size reduction factor in the first step allows us to simultaneously bootstrap a spanner and a dynamic APSP data structure. Notably, our approach does not need expander graphs, an otherwise ubiquitous tool in derandomization.
Cite as

Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein. Bootstrapping Dynamic APSP via Sparsification. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 113:1-113:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kyng_et_al:LIPIcs.ESA.2025.113,
  author =	{Kyng, Rasmus and Meierhans, Simon and Z\"{o}cklein, Gernot},
  title =	{{Bootstrapping Dynamic APSP via Sparsification}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{113:1--113:15},
  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.2025.113},
  URN =		{urn:nbn:de:0030-drops-245826},
  doi =		{10.4230/LIPIcs.ESA.2025.113},
  annote =	{Keywords: Dynamic Graph Algorithms, Spanners, Vertex Sparsification, Bootstrapping}
}
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.53
Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs

Authors: Yu Chen and Zihan Tan

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

Abstract
We study vertex sparsification for preserving cuts. Given a graph G with a subset |T| = k of its vertices called terminals, a quality-q cut sparsifier is a graph G' that contains T, such that, for any partition (T₁,T₂) of T into non-empty subsets, the value of the min-cut in G' separating T₁ from T₂ is within factor q from the value of the min-cut in G separating T₁ from T₂. The construction of cut sparsifiers with good (small) quality and size has been a central problem in graph compression for years. Planar graphs and quasi-bipartite graphs are two important special families studied in this research direction. The main results in this paper are new cut sparsifier constructions for them in the high-quality regime (where q = 1 or 1+{ε} for small {ε} > 0). We first show that every planar graph admits a planar quality-(1+{ε}) cut sparsifier of size Õ(k/poly({ε})), which is in sharp contrast with the lower bound of 2^{Ω(k)} for the quality-1 case. We then show that every quasi-bipartite graph admits a quality-1 cut sparsifier of size 2^{Õ(k²)}. This is the second to improve over the doubly-exponential bound for general graphs (previously only planar graphs have been shown to have single-exponential size quality-1 cut sparsifiers). Lastly, we show that contraction, a common approach for constructing cut sparsifiers adopted in most previous works, does not always give optimal bounds for cut sparsifiers. We demonstrate this by showing that the optimal size bound for quality-(1+{ε}) contraction-based cut sparsifiers for quasi-bipartite graphs lies in the range [k^{̃Ω(1/{ε})},k^{O(1/{ε}²)}], while in previous work an upper bound of Õ(k/{ε}²) was achieved via a non-contraction approach.
Cite as

Yu Chen and Zihan Tan. Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2025.53,
  author =	{Chen, Yu and Tan, Zihan},
  title =	{{Cut-Preserving Vertex Sparsifiers for Planar and Quasi-Bipartite Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{53:1--53:20},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-234304},
  doi =		{10.4230/LIPIcs.ICALP.2025.53},
  annote =	{Keywords: Termianl Cut, Graph Sparsification}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.77
Minimizing Recourse in an Adaptive Balls and Bins Game

Authors: Adi Fine, Haim Kaplan, and Uri Stemmer

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

Abstract
We consider a simple load-balancing game between an algorithm and an adaptive adversary. In a simplified version of this game, the adversary observes the assignment of jobs to machines and selects a machine to kill. The algorithm must then restart the jobs from the failed machine on other machines. The adversary repeats this process, observing the new assignment and eliminating another machine, and so on. The adversary aims to force the algorithm to perform many restarts, while we seek a robust algorithm that minimizes restarts regardless of the adversary’s strategy. This game was recently introduced by Bhattacharya et al. for designing a 3-spanner with low recourse against an adaptive adversary. We prove that a simple algorithm, which assigns each job to a randomly chosen live bin, incurs O(n log n) recourse against an adaptive adversary. This enables us to construct a much simpler 3-spanner with a recourse that is smaller by a factor of O(log² n) compared to the previous construction, without increasing the update time or the size of the spanner. This motivates a careful examination of the range of attacks an adaptive adversary can deploy against simple algorithms before resorting to more complex ones. As our case study demonstrates, this attack space may not be as large as it initially appears, enabling the development of robust algorithms that are both simpler and easier to analyze.
Cite as

Adi Fine, Haim Kaplan, and Uri Stemmer. Minimizing Recourse in an Adaptive Balls and Bins Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 77:1-77:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fine_et_al:LIPIcs.ICALP.2025.77,
  author =	{Fine, Adi and Kaplan, Haim and Stemmer, Uri},
  title =	{{Minimizing Recourse in an Adaptive Balls and Bins Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{77:1--77:19},
  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.2025.77},
  URN =		{urn:nbn:de:0030-drops-234544},
  doi =		{10.4230/LIPIcs.ICALP.2025.77},
  annote =	{Keywords: Adaptive adversary, load-balancing game, balls-and-bins, randomized algorithms, dynamic 3-spanner, dynamic graph algorithms, adversarial robustness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.111
A Simple Dynamic Spanner via APSP

Authors: Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein

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

Abstract
We give a simple algorithm for maintaining a n^{o(1)}-approximate spanner H of a graph G with n vertices as G receives edge updates by reduction to the dynamic All-Pairs Shortest Paths (APSP) problem. Given an initially empty graph G, our algorithm processes m insertions and n deletions in total time m^{1 + o(1)} and maintains an initially empty spanner H with total recourse n^{1 + o(1)}. When the number of insertions is much larger than the number of deletions, this notably yields recourse sub-linear in the total number of updates. Our simple algorithm can be extended to maintain a δ ≥ ω(1)-approximate spanner with n^{1+o(1)} edges throughout a sequence of m insertions and D deletions with amortized update time n^{o(1)} and total recourse n^{1 + o(1)} + n^{o(1)} ⋅ D via batching.
Cite as

Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein. A Simple Dynamic Spanner via APSP. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 111:1-111:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kyng_et_al:LIPIcs.ICALP.2025.111,
  author =	{Kyng, Rasmus and Meierhans, Simon and Z\"{o}cklein, Gernot},
  title =	{{A Simple Dynamic Spanner via APSP}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{111:1--111:11},
  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.2025.111},
  URN =		{urn:nbn:de:0030-drops-234886},
  doi =		{10.4230/LIPIcs.ICALP.2025.111},
  annote =	{Keywords: Dynamic graph algorithms, Spanner, Dynamic Greedy Spanner}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.132
Near-Optimal Algorithm for Directed Expander Decompositions

Authors: Aurelio L. Sulser and Maximilian Probst Gutenberg

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

Abstract
In this work, we present the first algorithm to compute expander decompositions in an m-edge directed graph with near-optimal time Õ(m). Further, our algorithm can maintain such a decomposition in a dynamic graph and again obtains near-optimal update times. Our result improves over previous algorithms [Bernstein et al., 2020; Hua et al., 2023] that only obtained algorithms optimal up to subpolynomial factors. In order to obtain our new algorithm, we present a new push-pull-relabel flow framework that generalizes the classic push-relabel flow algorithm [Goldberg and Tarjan, 1988] which was later dynamized for computing expander decompositions in undirected graphs [Henzinger et al., 2020; Saranurak and Wang, 2019]. We then show that the flow problems formulated in recent work [Hua et al., 2023] to decompose directed graphs can be solved much more efficiently in the push-pull-relabel flow framework. Recently, our algorithm has already been employed to obtain the currently fastest algorithm to compute min-cost flows [Van Den Brand et al., 2024]. We further believe that our algorithm can be used to speed-up and simplify recent breakthroughs in combinatorial graph algorithms towards fast maximum flow algorithms [Chuzhoy and Khanna, 2024; Chuzhoy and Khanna, 2024; Bernstein et al., 2024].
Cite as

Aurelio L. Sulser and Maximilian Probst Gutenberg. Near-Optimal Algorithm for Directed Expander Decompositions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 132:1-132:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sulser_et_al:LIPIcs.ICALP.2025.132,
  author =	{Sulser, Aurelio L. and Gutenberg, Maximilian Probst},
  title =	{{Near-Optimal Algorithm for Directed Expander Decompositions}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{132:1--132:20},
  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.2025.132},
  URN =		{urn:nbn:de:0030-drops-235096},
  doi =		{10.4230/LIPIcs.ICALP.2025.132},
  annote =	{Keywords: Directed Expander Decomposition, Push-Pull-Relabel Algorithm}
}
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}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.92
Fully Dynamic Algorithms for Transitive Reduction

Authors: Gramoz Goranci, Adam Karczmarz, Ali Momeni, and Nikos Parotsidis

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

Abstract
Given a directed graph G, a transitive reduction G^t of G (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of G that preserves the reachability relation between every two vertices in G. In this paper, we study the computational complexity of transitive reduction in the dynamic setting. We obtain the first fully dynamic algorithms for maintaining a transitive reduction of a general directed graph undergoing updates such as edge insertions or deletions. Our first algorithm achieves O(m+n log n) amortized update time, which is near-optimal for sparse directed graphs, and can even support extended update operations such as inserting a set of edges all incident to the same vertex, or deleting an arbitrary set of edges. Our second algorithm relies on fast matrix multiplication and achieves O(m+ n^{1.585}) worst-case update time.
Cite as

Gramoz Goranci, Adam Karczmarz, Ali Momeni, and Nikos Parotsidis. Fully Dynamic Algorithms for Transitive Reduction. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 92:1-92:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goranci_et_al:LIPIcs.ICALP.2025.92,
  author =	{Goranci, Gramoz and Karczmarz, Adam and Momeni, Ali and Parotsidis, Nikos},
  title =	{{Fully Dynamic Algorithms for Transitive Reduction}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{92:1--92:20},
  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.2025.92},
  URN =		{urn:nbn:de:0030-drops-234697},
  doi =		{10.4230/LIPIcs.ICALP.2025.92},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
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