25 Search Results for "Schwartzman, Gregory"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.102
Smoothed Analysis of Dynamic Graph Algorithms

Authors: Uri Meir and Ami Paz

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

Abstract
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and Yu, FOCS 2023). As worst-case analysis (adversarial inputs) may lead to the necessity of high running times, a natural question arises: in which cases are high running times really necessary, and in which cases these inputs merely manifest unique pathological cases? Early attempts to tackle this question were made by Nikoletseas, Reif, Spirakis and Yung (ICALP 1995) and by Alberts and Henzinger (Algorithmica 1998), who considered models with very little adversarial control over the inputs, and showed fast algorithms exist for them. The question was then overlooked for decades, until Henzinger, Lincoln and Saha (SODA 2022) recently addressed uniformly random inputs, and presented algorithms and impossibility results for several subgraph counting problems. To tackle the above question more thoroughly, we employ smoothed analysis, a celebrated framework introduced by Spielman and Teng (J. ACM, 2004). An input is proposed by an adversary but then a noisy version of it is processed by the algorithm instead. This model of inputs is parameterized by the amount of adversarial control, and fully interpolates between worst-case inputs and a uniformly random input. Doing so, we extend impossibility results for some problems to the smoothed model with only a minor quantitative loss. That is, we show that partially-adversarial inputs suffice to impose high running times for certain problems. In contrast, we show that other problems become easy even with the slightest amount of noise. In addition, we study the interplay between the adversary and the noise, leading to three natural models of smoothed inputs, for which we show a hierarchy of increasing difficulty stretching between the average-case and the worst-case complexities.
Cite as

Uri Meir and Ami Paz. Smoothed Analysis of Dynamic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{meir_et_al:LIPIcs.ITCS.2026.102,
  author =	{Meir, Uri and Paz, Ami},
  title =	{{Smoothed Analysis of Dynamic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{102:1--102:20},
  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.2026.102},
  URN =		{urn:nbn:de:0030-drops-253896},
  doi =		{10.4230/LIPIcs.ITCS.2026.102},
  annote =	{Keywords: Dynamic graph algorithms, Smoothed analysis, Shortest paths}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.10
Computing in a Faulty Congested Clique

Authors: Keren Censor-Hillel and Pedro Soto

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
We study a Faulty Congested Clique model, in which an adversary may fail nodes in the network throughout the computation. We show that any task of O(nlog{n})-bit input per node can be solved in roughly n rounds, where n is the size of the network. This nearly matches the linear upper bound on the complexity of the non-faulty Congested Clique model for such problems, by learning the entire input, and it holds in the faulty model even with a linear number of faults. Our main contribution is that we establish that one can do much better by looking more closely at the computation. Given a deterministic algorithm 𝒜 for the non-faulty Congested Clique model, we show how to transform it into an algorithm 𝒜' for the faulty model, with an overhead that could be as small as some logarithmic-in-n factor, by considering refined complexity measures of 𝒜. As an exemplifying application of our approach, we show that the O(n^{1/3})-round complexity of semi-ring matrix multiplication [Censor{-}Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela, PODC 2015] remains the same up to polylog factors in the faulty model, even if the adversary can fail 99% of the nodes (or any other constant fraction).
Cite as

Keren Censor-Hillel and Pedro Soto. Computing in a Faulty Congested Clique. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2025.10,
  author =	{Censor-Hillel, Keren and Soto, Pedro},
  title =	{{Computing in a Faulty Congested Clique}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.10},
  URN =		{urn:nbn:de:0030-drops-251833},
  doi =		{10.4230/LIPIcs.OPODIS.2025.10},
  annote =	{Keywords: distributed computing, graph algorithms, computing with faults}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.23
Distributed (Δ+1)-Coloring in Graphs of Bounded Neighborhood Independence

Authors: Marc Fuchs and Fabian Kuhn

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
The distributed coloring problem is arguably one of the key problems studied in the area of distributed graph algorithms. The most standard variant of the problem asks for a proper vertex coloring of a graph with Δ+1 colors, where Δ is the maximum degree of the graph. Despite an immense amount of work on distributed coloring problems in the distributed setting, determining the deterministic complexity of (Δ+1)-coloring in the standard message passing model remains one of the most important open questions of the area. In the LOCAL model, it is known that (Δ+1)-coloring requires Ω(log^* n) rounds even in paths and rings (i.e., when Δ = 2). For general graphs, the problem is known to be solvable in Õ(log^{5/3}n) rounds and in O(√{ΔlogΔ} + log^* n) rounds when expressing the complexity as a function of Δ and with an optimal dependency on n. In the present paper, we aim to improve our understanding of the deterministic complexity of (Δ+1)-coloring as a function of Δ in a special family of graphs for which significantly faster algorithms are already known. The neighborhood independence θ of a graph is the maximum number of pairwise non-adjacent neighbors of some node of the graph. Notable examples of graphs of bounded neighborhood independence are line graphs of graphs and bounded-rank hypergraphs. It is known that the (2Δ-1)-edge coloring problem and therefore the (Δ+1)-coloring problem in line graphs of graphs can be solved in O(log^{12}Δ+log^* n) rounds. In general, in graphs of neighborhood independence θ = O(1), it is known that (Δ+1)-coloring can be solved in 2^{O(√{logΔ})}+O(log^* n) rounds. In the present paper, we significantly improve the latter result, and we show that in graphs of neighborhood independence θ, a (Δ+1)-coloring can be computed in (θ⋅logΔ)^{O(log logΔ / log log logΔ)}+O(log^* n) rounds and thus in quasipolylogarithmic time in Δ as long as θ is at most polylogarithmic in Δ. Our algorithm can be seen as a generalization of an existing similar, but slightly weaker result for (2Δ-1)-edge coloring. We also show that the approach that leads to this polylogarithmic in Δ algorithm for (2Δ-1)-edge coloring already fails for edge colorings of hypergraphs of rank at least 3. At the core of the fast edge coloring algorithm is an algorithm to divide the edges of a graph into two parts so that up to a multiplicative error of 1+o(1), the maximum degree of the line graph induced by each part is at most half the maximum degree of the original line graph. We show that computing such a bipartition of the edges of the line graph of a hypergraph of rank at least 3 requires time logarithmic in n.
Cite as

Marc Fuchs and Fabian Kuhn. Distributed (Δ+1)-Coloring in Graphs of Bounded Neighborhood Independence. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fuchs_et_al:LIPIcs.OPODIS.2025.23,
  author =	{Fuchs, Marc and Kuhn, Fabian},
  title =	{{Distributed (\Delta+1)-Coloring in Graphs of Bounded Neighborhood Independence}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.23},
  URN =		{urn:nbn:de:0030-drops-251968},
  doi =		{10.4230/LIPIcs.OPODIS.2025.23},
  annote =	{Keywords: distributed computing, distributed graph algorithms, graph coloring, list coloring, defective coloring}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.40
On the Randomized Locality of Matching Problems in Regular Graphs

Authors: Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang

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

Abstract
The main goal in distributed symmetry-breaking is to understand the locality of problems: the radius of the neighborhood that a node must explore to determine its part of a global solution. In this work, we study the locality of matching problems in the family of regular graphs, which is one of the main benchmarks for establishing lower bounds on the locality of symmetry-breaking problems, as well as for obtaining classification results. Our main results are summarized as follows: 1) Approximate matching: We develop randomized algorithms to show that (1 + ε)-approximate matching in regular graphs is truly local, i.e., the locality depends only on ε and is independent of all other graph parameters. Furthermore, as long as the degree Δ is not very small (namely, as long as Δ ≥ poly(1/ε)), this dependence is only logarithmic in 1/ε. This stands in sharp contrast to maximal matching in regular graphs which requires some dependence on the number of nodes n or the degree Δ. 2) Maximal matching: Our techniques further allow us to establish a strong separation between the node-averaged complexity and worst-case complexity of maximal matching in regular graphs, by showing that the former is only O(1). Central to our main technical contribution is a novel martingale-based analysis for the ≈ 40-year-old algorithm by Luby. In particular, our analysis shows that applying one round of Luby’s algorithm on the line graph of a Δ-regular graph results in an almost Δ/2-regular graph.
Cite as

Seri Khoury, Manish Purohit, Aaron Schild, and Joshua R. Wang. On the Randomized Locality of Matching Problems in Regular Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 40:1-40:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khoury_et_al:LIPIcs.DISC.2025.40,
  author =	{Khoury, Seri and Purohit, Manish and Schild, Aaron and Wang, Joshua R.},
  title =	{{On the Randomized Locality of Matching Problems in Regular Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{40:1--40:20},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-248570},
  doi =		{10.4230/LIPIcs.DISC.2025.40},
  annote =	{Keywords: regular graphs, maximum matching, augmenting paths, distributed algorithms, Luby’s algorithm, martingales}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.22
The Complexity Landscape of Dynamic Distributed Subgraph Finding

Authors: Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang

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

Abstract
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in nearly all settings. However, several open questions remain, and very little is known about finding subgraphs beyond cliques. In this work, we consider these questions and explore subgraphs beyond cliques in the deterministic setting. For finding cliques, we establish an Ω(log log n) bandwidth lower bound for one-round membership-detection under edge insertions only and an Ω(log log log n) bandwidth lower bound for one-round detection under both edge insertions and node insertions. Moreover, we demonstrate new algorithms to show that our lower bounds are tight in bounded-degree networks when the target subgraph is a triangle. Prior to our work, no lower bounds were known for these problems. For finding subgraphs beyond cliques, we present a complete characterization of the bandwidth complexity of the membership-listing problem for every target subgraph, every number of rounds, and every type of topological change: node insertions, node deletions, edge insertions, and edge deletions. We also show partial characterizations for one-round membership-detection and listing.
Cite as

Yi-Jun Chang, Lyuting Chen, Yanyu Chen, Gopinath Mishra, and Mingyang Yang. The Complexity Landscape of Dynamic Distributed Subgraph Finding. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chang_et_al:LIPIcs.DISC.2025.22,
  author =	{Chang, Yi-Jun and Chen, Lyuting and Chen, Yanyu and Mishra, Gopinath and Yang, Mingyang},
  title =	{{The Complexity Landscape of Dynamic Distributed Subgraph Finding}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{22:1--22:20},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-248399},
  doi =		{10.4230/LIPIcs.DISC.2025.22},
  annote =	{Keywords: Distributed algorithms, dynamic algorithms, subgraph finding}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.54
Brief Announcement: Faster CONGEST Approximation Algorithms for Maximum Weighted Independent Set in Sparse Graphs

Authors: Salwa Faour and Fabian Kuhn

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

Abstract
The maximum independent set problem is a classic optimization problem in graph theory that has also been studied quite intensively in the distributed setting. Although the problem is hard to approximate within reasonable factors in general, there are good approximation algorithms known for several sparse graph families. In the present paper, we consider deterministic distributed CONGEST algorithms for the weighted version of the problem in trees and graphs of bounded arboricity (i.e., hereditary sparse graphs). For trees, we prove that the task of deterministically computing a (1-ε)-approximate solution to the maximum weight independent set (MWIS) problem has a tight Θ(log^*(n) / ε) complexity. The lower bound already holds on unweighted oriented paths. On the upper bound side, we show that the bound can be achieved even in unrooted trees. For graphs G = (V,E) of arboricity β > 1, we give two algorithms. If the sum of all node weights is w(V), we show that for any ε > 0, an independent set of weight at least (1-ε)⋅(w(V))/(4β) can be computed in O(log²(β/ε)/ε + log^* n) rounds. This result is obtained by a direct application of the local rounding framework of Faour, Ghaffari, Grunau, Kuhn, and Rozhoň [SODA ‘23]. We further show that for any ε > 0, an independent set of weight at least (1-ε)⋅(w(V))/(2β+1) can be computed in O(log³(β)⋅log(1/ε)/ε² ⋅log n) rounds. For ε = ω(1/√{β}), this significantly improves on a recent result of Gil [OPODIS ‘23], who showed that a 1/⌊(2+ε)β⌋-approximation to the MWIS problem can be computed in O(β/ε⋅log n) rounds. As an intermediate step to our result, we design an algorithm to compute an independent set of total weight at least (1-ε)⋅∑_{v ∈ V}(w(v))/(deg(v)+1) in time O(log³(Δ)⋅log(1/ε)/ε + log^* n), where Δ is the maximum degree of the graph.
Cite as

Salwa Faour and Fabian Kuhn. Brief Announcement: Faster CONGEST Approximation Algorithms for Maximum Weighted Independent Set in Sparse Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 54:1-54:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{faour_et_al:LIPIcs.DISC.2025.54,
  author =	{Faour, Salwa and Kuhn, Fabian},
  title =	{{Brief Announcement: Faster CONGEST Approximation Algorithms for Maximum Weighted Independent Set in Sparse Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{54:1--54:7},
  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.2025.54},
  URN =		{urn:nbn:de:0030-drops-248704},
  doi =		{10.4230/LIPIcs.DISC.2025.54},
  annote =	{Keywords: CONGEST model, weighted independent set, approximation, trees, arboricity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.79
Semi-Streaming Algorithms for Hypergraph Matching

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

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

Abstract
We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.
Cite as

Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-Streaming Algorithms for Hypergraph Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2025.79,
  author =	{Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
  title =	{{Semi-Streaming Algorithms for Hypergraph Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{79:1--79:19},
  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.2025.79},
  URN =		{urn:nbn:de:0030-drops-245478},
  doi =		{10.4230/LIPIcs.ESA.2025.79},
  annote =	{Keywords: hypergraph, matching, semi-streaming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.17
Weighted Matching in a Poly-Streaming Model

Authors: Ahammed Ullah, S M Ferdous, and Alex Pothen

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

Abstract
We introduce the poly-streaming model, a generalization of streaming models of computation in which k processors process k data streams containing a total of N items. The algorithm is allowed 𝒪(f(k)⋅M₁) space, where M₁ is either o (N) or the space bound for a sequential streaming algorithm. Processors may communicate as needed. Algorithms are assessed by the number of passes, per-item processing time, total runtime, space usage, communication cost, and solution quality. We design a single-pass algorithm in this model for approximating the maximum weight matching (MWM) problem. Given k edge streams and a parameter ε > 0, the algorithm computes a (2+ε)-approximate MWM. We analyze its performance in a shared-memory parallel setting: for any constant ε > 0, it runs in time 𝒪̃(L_{max}+n), where n is the number of vertices and L_{max} is the maximum stream length. It supports 𝒪(1) per-edge processing time using 𝒪̃(k⋅n) space. We further generalize the design to hierarchical architectures, in which k processors are partitioned into r groups, each with its own shared local memory. The total intergroup communication is 𝒪̃(r⋅n) bits, while all other performance guarantees are preserved. We evaluate the algorithm on a shared-memory system using graphs with trillions of edges. It achieves substantial speedups as k increases and produces matchings with weights significantly exceeding the theoretical guarantee. On our largest test graph, it reduces runtime by nearly two orders of magnitude and memory usage by five orders of magnitude compared to an offline algorithm.
Cite as

Ahammed Ullah, S M Ferdous, and Alex Pothen. Weighted Matching in a Poly-Streaming Model. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ullah_et_al:LIPIcs.ESA.2025.17,
  author =	{Ullah, Ahammed and Ferdous, S M and Pothen, Alex},
  title =	{{Weighted Matching in a Poly-Streaming Model}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{17:1--17:18},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-244858},
  doi =		{10.4230/LIPIcs.ESA.2025.17},
  annote =	{Keywords: Streaming Algorithms, Matchings, Graphs, Parallel Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.19
Dynamic Algorithms for Submodular Matching

Authors: Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh

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

Abstract
The Maximum Submodular Matching (MSM) problem is a generalization of the classical Maximum Weight Matching (MWM) problem. In this problem, given a monotone submodular function f: 2^E → ℝ^{≥ 0} defined over subsets of edges of a graph G(V, E), we are asked to return a matching whose submodular value is maximum among all matchings in graph G(V, E). In this paper, we consider this problem in a fully dynamic setting against an oblivious adversary. In this setting, we are given a sequence 𝒮 of insertions and deletions of edges of the underlying graph G(V, E), along with an oracle access to the monotone submodular function f. The goal is to maintain a matching M such that, at any time t of sequence 𝒮, its submodular value is a good approximation of the value of the optimal submodular matching while keeping the number of operations minimal. We develop the first dynamic algorithm for the submodular matching problem, in which we maintain a matching whose submodular value is within expected (8 + ε)-approximation of the optimal submodular matching at any time t of sequence 𝒮 using expected amortized poly(log n, 1/(ε)) update time. Our approach incorporates a range of novel techniques, notably the concept of Uniform Hierarchical Caches (UHC) data structure along with its invariants, which lead to the first algorithm for fully dynamic submodular matching and may be of independent interest for designing dynamic algorithms for other problems.
Cite as

Kiarash Banihashem, Leyla Biabani, Samira Goudarzi, MohammadTaghi Hajiaghayi, Peyman Jabbarzade, and Morteza Monemizadeh. Dynamic Algorithms for Submodular Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 19:1-19:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{banihashem_et_al:LIPIcs.ICALP.2025.19,
  author =	{Banihashem, Kiarash and Biabani, Leyla and Goudarzi, Samira and Hajiaghayi, MohammadTaghi and Jabbarzade, Peyman and Monemizadeh, Morteza},
  title =	{{Dynamic Algorithms for Submodular Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{19:1--19:21},
  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.2025.19},
  URN =		{urn:nbn:de:0030-drops-233969},
  doi =		{10.4230/LIPIcs.ICALP.2025.19},
  annote =	{Keywords: Matching, Submodular, Dynamic, Polylogarithmic}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.135
Deterministic Independent Sets in the Semi-Streaming Model

Authors: Daniel Ye

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

Abstract
We consider the independent set problem in the semi-streaming model. For any input graph G = (V, E) with n vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, G is presented as a stream of edges and any algorithm must use Õ(n) bits of memory to output a large independent set at the end of the stream. Prior work has designed various semi-streaming algorithms for finding independent sets. Due to the hardness of finding maximum and maximal independent sets in the semi-streaming model, the focus has primarily been on finding independent sets in terms of certain parameters, such as the maximum degree Δ. In particular, there is a simple randomized algorithm that obtains independent sets of size n/(Δ+1) in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. The best we know is a straightforward algorithm that finds an Ω̃(n/(Δ²)) size independent set. We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an Õ(n/(Δ²)) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem.
Cite as

Daniel Ye. Deterministic Independent Sets in the Semi-Streaming Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 135:1-135:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ye:LIPIcs.ICALP.2025.135,
  author =	{Ye, Daniel},
  title =	{{Deterministic Independent Sets in the Semi-Streaming Model}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{135:1--135:17},
  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.2025.135},
  URN =		{urn:nbn:de:0030-drops-235129},
  doi =		{10.4230/LIPIcs.ICALP.2025.135},
  annote =	{Keywords: Sublinear Algorithms, Derandomization, Semi-Streaming Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.119
Faster Semi-Streaming Matchings via Alternating Trees

Authors: Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu

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

Abstract
We design a deterministic algorithm for the (1+ε)-approximate maximum matching problem. Our primary result demonstrates that this problem can be solved in O(ε^{-6}) semi-streaming passes, improving upon the O(ε^{-19}) pass-complexity algorithm by [Fischer, Mitrović, and Uitto, STOC'22]. This contributes substantially toward resolving Open question 2 from [Assadi, SOSA'24]. Leveraging the framework introduced in [FMU'22], our algorithm achieves an analogous round complexity speed-up for computing a (1+ε)-approximate maximum matching in both the Massively Parallel Computation (MPC) and CONGEST models. The data structures maintained by our algorithm are formulated using blossom notation and represented through alternating trees. This approach enables a simplified correctness analysis by treating specific components as if operating on bipartite graphs, effectively circumventing certain technical intricacies present in prior work.
Cite as

Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu. Faster Semi-Streaming Matchings via Alternating Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 119:1-119:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mitrovic_et_al:LIPIcs.ICALP.2025.119,
  author =	{Mitrovi\'{c}, Slobodan and Mukherjee, Anish and Sankowski, Piotr and Sheu, Wen-Horng},
  title =	{{Faster Semi-Streaming Matchings via Alternating Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{119:1--119:19},
  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.2025.119},
  URN =		{urn:nbn:de:0030-drops-234965},
  doi =		{10.4230/LIPIcs.ICALP.2025.119},
  annote =	{Keywords: streaming algorithms, approximation algorithms, maximum matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.9
Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model

Authors: Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the (1,2)-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on the closely related Maximum Path Cover Problem, which aims to find a collection of vertex-disjoint paths that covers the maximum number of edges in a graph. We propose an algorithm that, for any ε > 0, achieves a (2/3-ε)-approximation of the maximum path cover size for an n-vertex graph, using poly(1/ε) passes. This result improves upon the previous 1/2-approximation by Behnezhad et al. [Soheil Behnezhad et al., 2023] in the semi-streaming model. Building on this result, we design a semi-streaming algorithm that constructs a tour for an instance of (1,2)-TSP with an approximation factor of (4/3 + ε), improving upon the previous 3/2-approximation factor algorithm by Behnezhad et al. [Soheil Behnezhad et al., 2023]. Furthermore, we extend our approach to develop an approximation algorithm for the Maximum TSP (Max-TSP), where the goal is to find a Hamiltonian cycle with the maximum possible weight in a given weighted graph G. Our algorithm provides a (7/12 - ε)-approximation for Max-TSP in poly(1/(ε)) passes, improving on the previously known (1/2-ε)-approximation obtained via maximum weight matching in the semi-streaming model.
Cite as

Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke. Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alipour_et_al:LIPIcs.STACS.2025.9,
  author =	{Alipour, Sharareh and Farokhnejad, Ermiya and M\"{o}mke, Tobias},
  title =	{{Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.9},
  URN =		{urn:nbn:de:0030-drops-228342},
  doi =		{10.4230/LIPIcs.STACS.2025.9},
  annote =	{Keywords: (1,2)-TSP, Max-TSP, Maximum Path Cover, Semi-Streaming Algorithms, Approximation Algorithms, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.45
Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs

Authors: Jinfeng Dou, Thorsten Götte, Henning Hillebrandt, Christian Scheideler, and Julian Werthmann

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We consider the distributed and parallel construction of low-diameter decompositions with strong diameter. We present algorithms for arbitrary undirected, weighted graphs and also for undirected, weighted graphs that can be separated through k ∈ Õ(1) shortest paths. This class of graphs includes planar graphs, graphs of bounded treewidth, and graphs that exclude a fixed minor K_r. Our algorithms work in the PRAM, CONGEST, and the novel HYBRID communication model and are competitive in all relevant parameters. Given 𝒟 > 0, our low-diameter decomposition algorithm divides the graph into connected clusters of strong diameter 𝒟. For an arbitrary graph, an edge e ∈ E of length 𝓁_e is cut between two clusters with probability O(𝓁_e⋅log(n)/𝒟). If the graph can be separated by k ∈ Õ(1) paths, the probability improves to O(𝓁_e⋅log(log n)/𝒟). In either case, the decompositions can be computed in Õ(1) depth and Õ(m) work in the PRAM and Õ(1) time in the HYBRID model. In CONGEST, the runtimes are Õ(HD + √n) and Õ(HD) respectively. All these results hold w.h.p. Broadly speaking, we present distributed and parallel implementations of sequential divide-and-conquer algorithms where we replace exact shortest paths with approximate shortest paths. In contrast to exact paths, these can be efficiently computed in the distributed and parallel setting [STOC '22]. Further, and perhaps more importantly, we show that instead of explicitly computing vertex-separators to enable efficient parallelization of these algorithms, it suffices to sample a few random paths of bounded length and the nodes close to them. Thereby, we do not require complex embeddings whose implementation is unknown in the distributed and parallel setting.
Cite as

Jinfeng Dou, Thorsten Götte, Henning Hillebrandt, Christian Scheideler, and Julian Werthmann. Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 45:1-45:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dou_et_al:LIPIcs.ITCS.2025.45,
  author =	{Dou, Jinfeng and G\"{o}tte, Thorsten and Hillebrandt, Henning and Scheideler, Christian and Werthmann, Julian},
  title =	{{Distributed and Parallel Low-Diameter Decompositions for Arbitrary and Restricted Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{45:1--45:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.45},
  URN =		{urn:nbn:de:0030-drops-226734},
  doi =		{10.4230/LIPIcs.ITCS.2025.45},
  annote =	{Keywords: Distributed Graph Algorithms, Network Decomposition, Excluded Minor}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.33
Self-Stabilizing Fully Adaptive Maximal Matching

Authors: Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
A self-stabilizing randomized algorithm for mending maximal matching (MM) in synchronous networks is presented. Starting from a legal MM configuration and assuming that the network undergoes k faults or topology changes (that may occur in multiple batches), the algorithm is guaranteed to stabilize back to a legal MM configuration in time O(log k) in expectation and with high probability (in k), using constant size messages. The algorithm is simple to implement and is uniform in the sense that it does not assume unique identifiers, nor does it assume any global knowledge of the communication graph including its size. It relies on a generic probabilistic phase synchronization technique that may be useful for other self-stabilizing problems. The algorithm compares favorably with the existing self-stabilizing MM algorithms in terms of the dependence of its run-time on k, a.k.a. fully adaptive run-time. In fact, this dependence is asymptotically optimal for uniform algorithms that use constant size messages.
Cite as

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Self-Stabilizing Fully Adaptive Maximal Matching. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bitton_et_al:LIPIcs.OPODIS.2024.33,
  author =	{Bitton, Shimon and Emek, Yuval and Izumi, Taisuke and Kutten, Shay},
  title =	{{Self-Stabilizing Fully Adaptive Maximal Matching}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{33:1--33:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.33},
  URN =		{urn:nbn:de:0030-drops-225698},
  doi =		{10.4230/LIPIcs.OPODIS.2024.33},
  annote =	{Keywords: self-stabilization, maximal matching, fully adaptive run-time, dynamic graphs}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2024.36
Distributed Branching Random Walks and Their Applications

Authors: Vijeth Aradhya, Seth Gilbert, and Thorsten Götte

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract
In recent years, the explosion of big data and analytics has necessitated distributed storage and processing with several compute nodes (e.g., multiple datacenters). These nodes collaboratively perform parallel computation, where the data is typically partitioned across these nodes to ensure scalability, redundancy and load-balancing. But the nodes may not always be co-located; in many cases, they are part of a larger communication network. Since those nodes only need to communicate among themselves, a key challenge is to design efficient routes catered to that subnetwork. In this work, we initiate the study of distributed sampling and routing problems for subnetworks in any well-connected network. Given any network G = (V, E) with mixing time τ_mix, consider the canonical problem of permutation routing [Ghaffari, Kuhn and Su, PODC 2017] that aims to minimize both congestion and dilation of the routes, where the demands (i.e., set of source-terminal pairs) are such that each node sends or receives number of messages proportional to its degree. We show that the permutation routing problem, when demands are restricted to any subset S ⊆ V (i.e., subnetwork), can be solved in exp(O(√(log|S|))) ⋅ Õ(τ_mix) rounds (where Õ(⋅) hides polylogarithmic factors of |V|). This means that the running time depends subpolynomially on the subnetwork size (i.e., not on the entire network size). The ability to solve permutation routing efficiently immediately implies that a large class of parallel algorithms can be simulated efficiently on the subnetwork. As a prerequisite to constructing efficient routes, we design and analyze distributed branching random walks that distribute tokens started by the nodes in the subnetwork. At a high-level, these algorithms operate by always moving each token according to a (lazy) simple random walk, but also branching a token into multiple tokens at some specified intervals; ultimately, if a node starts a branching walk, with its id in a token, then by the end of execution, several tokens with its id would be randomly distributed among the nodes. As these random walks can be started by many nodes, a crucial challenge is to ensure low-congestion, which is a primary focus of this paper.
Cite as

Vijeth Aradhya, Seth Gilbert, and Thorsten Götte. Distributed Branching Random Walks and Their Applications. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aradhya_et_al:LIPIcs.OPODIS.2024.36,
  author =	{Aradhya, Vijeth and Gilbert, Seth and G\"{o}tte, Thorsten},
  title =	{{Distributed Branching Random Walks and Their Applications}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{36:1--36:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.36},
  URN =		{urn:nbn:de:0030-drops-225723},
  doi =		{10.4230/LIPIcs.OPODIS.2024.36},
  annote =	{Keywords: Distributed Graph Algorithms, Random Walks, Permutation Routing}
}
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