41 Search Results for "Ghaffari, Mohsen"

Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2024.2
Simple (Invited Talk)

Authors: Eva Rotenberg

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Simplicity in algorithms has various aspects; interpretations and implications. One is the simplicity of the algorithmic solution itself: if an algorithm (or data structure) has a brief verbal description or can be written with few lines of pseudocode, this can lead to easier, more robust, and possibly more efficient implementations. Another aspect of simplicity relates to the proofs of correctness and efficiency of our algorithmic solutions. Here, we experience that algorithms and data structures with simpler proofs of statements about their properties can be easier to understand, easier to teach, and sometimes, easier to generalise. Simplification of proofs also receives attention in mathematics; here, too, simplification has benefits to clarity of exposition and possibility of generalisation. There are even examples of proof simplification leading to the design of new and more efficient algorithms. This talk will present examples illustrating these various aspects of simplicity. Examples where algorithmic simplification or proof simplification has led to improved performance of algorithms and data structures, in theory, in practice, or both. Finally, some of the most attractive questions in discrete mathematics and in theory of computing have a property in common: they are very simple to pose, but surprisingly, to our knowledge, not very simple to answer. The talk will include examples of such questions, which I leave as an open problem for the audience.
Cite as

Eva Rotenberg. Simple (Invited Talk). In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 2:1-2:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{rotenberg:LIPIcs.ESA.2024.2,
  author =	{Rotenberg, Eva},
  title =	{{Simple}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{2:1--2:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.2},
  URN =		{urn:nbn:de:0030-drops-210739},
  doi =		{10.4230/LIPIcs.ESA.2024.2},
  annote =	{Keywords: Simplicity, graph algorithms, computational geometry, algorithmic simplification, data structures, combinatorics, proof simplification, dynamic graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.13
Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights

Authors: Vikrant Ashvinkumar, Aaron Bernstein, Nairen Cao, Christoph Grunau, Bernhard Haeupler, Yonggang Jiang, Danupon Nanongkai, and Hsin-Hao Su

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
This paper presents parallel, distributed, and quantum algorithms for single-source shortest paths when edges can have negative integer weights (negative-weight SSSP). We show a framework that reduces negative-weight SSSP in all these settings to n^{o(1)} calls to any SSSP algorithm that works on inputs with non-negative integer edge weights (non-negative-weight SSSP) with a virtual source. More specifically, for a directed graph with m edges, n vertices, undirected hop-diameter D, and polynomially bounded integer edge weights, we show randomized algorithms for negative-weight SSSP with - W_{SSSP}(m,n)n^{o(1)} work and S_{SSSP}(m,n)n^{o(1)} span, given access to a non-negative-weight SSSP algorithm with W_{SSSP}(m,n) work and S_{SSSP}(m,n) span in the parallel model, and - T_{SSSP}(n,D)n^{o(1)} rounds, given access to a non-negative-weight SSSP algorithm that takes T_{SSSP}(n,D) rounds in CONGEST, and - Q_{SSSP}(m,n)n^{o(1)} quantum edge queries, given access to a non-negative-weight SSSP algorithm that takes Q_{SSSP}(m,n) queries in the quantum edge query model. This work builds off the recent result of Bernstein, Nanongkai, Wulff-Nilsen [Bernstein et al., 2022], which gives a near-linear time algorithm for negative-weight SSSP in the sequential setting. Using current state-of-the-art non-negative-weight SSSP algorithms yields randomized algorithms for negative-weight SSSP with - m^{1+o(1)} work and n^{1/2+o(1)} span in the parallel model, and - (n^{2/5}D^{2/5} + √n + D)n^{o(1)} rounds in CONGEST, and - m^{1/2}n^{1/2+o(1)} quantum queries to the adjacency list or n^{1.5+o(1)} quantum queries to the adjacency matrix. Up to a n^{o(1)} factor, the parallel and distributed results match the current best upper bounds for reachability [Jambulapati et al., 2019; Cao et al., 2021]. Consequently, any improvement to negative-weight SSSP in these models beyond the n^{o(1)} factor necessitates an improvement to the current best bounds for reachability. The quantum result matches the lower bound up to an n^{o(1)} factor [Aija Berzina et al., 2004]. Our main technical contribution is an efficient reduction from computing a low-diameter decomposition (LDD) of directed graphs to computations of non-negative-weight SSSP with a virtual source. Efficiently computing an LDD has heretofore only been known for undirected graphs in both the parallel and distributed models, and been rather unstudied in quantum models. The directed LDD is a crucial step of the sequential algorithm in [Bernstein et al., 2022], and we think that its applications to other problems in parallel and distributed models are far from being exhausted. Other ingredients of our results include altering the recursion structure of the scaling algorithm in [Bernstein et al., 2022] to surmount difficulties that arise in these models, and also an efficient reduction from computing strongly connected components to computations of SSSP with a virtual source in CONGEST. The latter result answers a question posed in [Bernstein and Nanongkai, 2019] in the negative.
Cite as

Vikrant Ashvinkumar, Aaron Bernstein, Nairen Cao, Christoph Grunau, Bernhard Haeupler, Yonggang Jiang, Danupon Nanongkai, and Hsin-Hao Su. Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ashvinkumar_et_al:LIPIcs.ESA.2024.13,
  author =	{Ashvinkumar, Vikrant and Bernstein, Aaron and Cao, Nairen and Grunau, Christoph and Haeupler, Bernhard and Jiang, Yonggang and Nanongkai, Danupon and Su, Hsin-Hao},
  title =	{{Parallel, Distributed, and Quantum Exact Single-Source Shortest Paths with Negative Edge Weights}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.13},
  URN =		{urn:nbn:de:0030-drops-210849},
  doi =		{10.4230/LIPIcs.ESA.2024.13},
  annote =	{Keywords: Parallel algorithm, distributed algorithm, shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.24
A Parameterized Algorithm for Vertex and Edge Connectivity of Embedded Graphs

Authors: Therese Biedl, Prosenjit Bose, and Karthik Murali

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
The problem of computing vertex and edge connectivity of a graph are classical problems in algorithmic graph theory. The focus of this paper is on computing these parameters for graphs drawn on the plane. A typical example of such graphs are planar graphs which can be embedded without any crossings. It has long been known that vertex and edge connectivity of planar embedded graphs can be computed in linear time. Very recently, Biedl and Murali extended the techniques from planar graphs to 1-plane graphs without ×-crossings, i.e., crossings whose endpoints induce a matching. While the tools used were novel, they were highly tailored to 1-plane graphs, and do not provide much leeway for further extension. In this paper, we develop alternate techniques that are simpler, have wider applications to near-planar graphs, and can be used to test both vertex and edge connectivity. Our technique works for all those embedded graphs where any pair of crossing edges are connected by a path that, roughly speaking, can be covered with few cells of the drawing. Important examples of such graphs include optimal 2-planar and optimal 3-planar graphs, d-map graphs, d-framed graphs, graphs with bounded crossing number, and k-plane graphs with bounded number of ×-crossings.
Cite as

Therese Biedl, Prosenjit Bose, and Karthik Murali. A Parameterized Algorithm for Vertex and Edge Connectivity of Embedded Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 24:1-24:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{biedl_et_al:LIPIcs.ESA.2024.24,
  author =	{Biedl, Therese and Bose, Prosenjit and Murali, Karthik},
  title =	{{A Parameterized Algorithm for Vertex and Edge Connectivity of Embedded Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{24:1--24:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.24},
  URN =		{urn:nbn:de:0030-drops-210950},
  doi =		{10.4230/LIPIcs.ESA.2024.24},
  annote =	{Keywords: Vertex Connectivity, Edge Connectivity, 1-planar, k-planar, Linear-time}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.41
Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing

Authors: Chandra Chekuri and Rhea Jain

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider two-cost network design models in which edges of the input graph have an associated cost and length. We build upon recent advances in hop-constrained oblivious routing to obtain two sets of results. We address multicommodity buy-at-bulk network design in the nonuniform setting. Existing poly-logarithmic approximations are based on the junction tree approach [Chekuri et al., 2010; Guy Kortsarz and Zeev Nutov, 2011]. We obtain a new polylogarithmic approximation via a natural LP relaxation. This establishes an upper bound on its integrality gap and affirmatively answers an open question raised in [Chekuri et al., 2010]. The rounding is based on recent results in hop-constrained oblivious routing [Ghaffari et al., 2021], and this technique yields a polylogarithmic approximation in more general settings such as set connectivity. Our algorithm for buy-at-bulk network design is based on an LP-based reduction to h-hop constrained network design for which we obtain LP-based bicriteria approximation algorithms. We also consider a fault-tolerant version of h-hop constrained network design where one wants to design a low-cost network to guarantee short paths between a given set of source-sink pairs even when k-1 edges can fail. This model has been considered in network design [Luis Gouveia and Markus Leitner, 2017; Gouveia et al., 2018; Arslan et al., 2020] but no approximation algorithms were known. We obtain polylogarithmic bicriteria approximation algorithms for the single-source setting for any fixed k. We build upon the single-source algorithm and the junction-tree approach to obtain an approximation algorithm for the multicommodity setting when at most one edge can fail.
Cite as

Chandra Chekuri and Rhea Jain. Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 41:1-41:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chekuri_et_al:LIPIcs.ESA.2024.41,
  author =	{Chekuri, Chandra and Jain, Rhea},
  title =	{{Approximation Algorithms for Hop Constrained and Buy-At-Bulk Network Design via Hop Constrained Oblivious Routing}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{41:1--41:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.41},
  URN =		{urn:nbn:de:0030-drops-211124},
  doi =		{10.4230/LIPIcs.ESA.2024.41},
  annote =	{Keywords: Buy-at-bulk, Hop-constrained network design, LP integrality gap, Fault-tolerant network design}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.53
Semi-Streaming Algorithms for Weighted k-Disjoint Matchings

Authors: S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We design and implement two single-pass semi-streaming algorithms for the maximum weight k-disjoint matching (k-DM) problem. Given an integer k, the k-DM problem is to find k pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For k ≥ 2, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is 1/(3+ε)-approximate. We also develop an approximation preserving reduction from k-DM to the maximum weight b-matching problem. Leveraging this reduction and an existing semi-streaming b-matching algorithm, we design a (1/(2+ε))(1 - 1/(k+1))-approximate semi-streaming algorithm for k-DM. For any constant ε > 0, both of these algorithms require O(nk log_{1+ε}² n) bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the k-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6× to 512× less) and were faster in runtime than the offline algorithms. Our solutions were often within 5% of the best weights from the offline algorithms. We highlight that the existing offline algorithms run out of 1 TB memory for most of the large instances (> 1 billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for k = 8.
Cite as

S M Ferdous, Bhargav Samineni, Alex Pothen, Mahantesh Halappanavar, and Bala Krishnamoorthy. Semi-Streaming Algorithms for Weighted k-Disjoint Matchings. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 53:1-53:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ferdous_et_al:LIPIcs.ESA.2024.53,
  author =	{Ferdous, S M and Samineni, Bhargav and Pothen, Alex and Halappanavar, Mahantesh and Krishnamoorthy, Bala},
  title =	{{Semi-Streaming Algorithms for Weighted k-Disjoint Matchings}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{53:1--53:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.53},
  URN =		{urn:nbn:de:0030-drops-211245},
  doi =		{10.4230/LIPIcs.ESA.2024.53},
  annote =	{Keywords: Matchings, Semi-Streaming Algorithms, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.89
Locally Computing Edge Orientations

Authors: Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider the question of orienting the edges in a graph G such that every vertex has bounded out-degree. For graphs of arboricity α, there is an orientation in which every vertex has out-degree at most α and, moreover, the best possible maximum out-degree of an orientation is at least α - 1. We are thus interested in algorithms that can achieve a maximum out-degree of close to α. A widely studied approach for this problem in the distributed algorithms setting is a "peeling algorithm" that provides an orientation with maximum out-degree α(2+ε) in a logarithmic number of iterations. We consider this problem in the local computation algorithm (LCA) model, which quickly answers queries of the form "What is the orientation of edge (u,v)?" by probing the input graph. When the peeling algorithm is executed in the LCA setting by applying standard techniques, e.g., the Parnas-Ron paradigm, it requires Ω(n) probes per query on an n-vertex graph. In the case where G has unbounded degree, we show that any LCA that orients its edges to yield maximum out-degree r must use Ω(√ n/r) probes to G per query in the worst case, even if G is known to be a forest (that is, α = 1). We also show several algorithms with sublinear probe complexity when G has unbounded degree. When G is a tree such that the maximum degree Δ of G is bounded, we demonstrate an algorithm that uses Δ n^{1-log_Δ r + o(1)} probes to G per query. To obtain this result, we develop an edge-coloring approach that ultimately yields a graph-shattering-like result. We also use this shattering-like approach to demonstrate an LCA which 4-colors any tree using sublinear probes per query.
Cite as

Slobodan Mitrović, Ronitt Rubinfeld, and Mihir Singhal. Locally Computing Edge Orientations. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 89:1-89:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mitrovic_et_al:LIPIcs.ESA.2024.89,
  author =	{Mitrovi\'{c}, Slobodan and Rubinfeld, Ronitt and Singhal, Mihir},
  title =	{{Locally Computing Edge Orientations}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{89:1--89:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.89},
  URN =		{urn:nbn:de:0030-drops-211603},
  doi =		{10.4230/LIPIcs.ESA.2024.89},
  annote =	{Keywords: local computation algorithms, edge orientation, tree coloring}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.5
Asynchronous Majority Dynamics on Binomial Random Graphs

Authors: Divyarthi Mohan and Paweł Prałat

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is correct with probability 1/2+δ for some δ > 0. At each round, a node is selected uniformly at random to update their public opinion to match the majority of their neighbours (breaking ties in favour of their initial private signal). Our main result shows that for sparse and connected binomial random graphs G(n,p) the process stabilizes in a correct consensus in 𝒪(nlog² n/log log n) steps with high probability. In fact, when log n/n ≪ p = o(1) the process terminates at time T^ = (1+o(1))nlog n, where T^ is the first time when all nodes have been selected at least once. However, in dense binomial random graphs with p = Ω(1), there is an information cascade where the process terminates in the incorrect consensus with probability bounded away from zero.
Cite as

Divyarthi Mohan and Paweł Prałat. Asynchronous Majority Dynamics on Binomial Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mohan_et_al:LIPIcs.APPROX/RANDOM.2024.5,
  author =	{Mohan, Divyarthi and Pra{\l}at, Pawe{\l}},
  title =	{{Asynchronous Majority Dynamics on Binomial Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.5},
  URN =		{urn:nbn:de:0030-drops-209985},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.5},
  annote =	{Keywords: Opinion dynamics, Social learning, Stochastic processes, Random Graphs, Consensus}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.16
Weighted Matching in the Random-Order Streaming and Robust Communication Models

Authors: Diba Hashemi and Weronika Wrzos-Kaminska

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the maximum weight matching problem in the random-order semi-streaming model and in the robust communication model. Unlike many other sublinear models, in these two frameworks, there is a large gap between the guarantees of the best known algorithms for the unweighted and weighted versions of the problem. In the random-order semi-streaming setting, the edges of an n-vertex graph arrive in a stream in a random order. The goal is to compute an approximate maximum weight matching with a single pass over the stream using O(npolylog n) space. Our main result is a (2/3-ε)-approximation algorithm for maximum weight matching in random-order streams, using space O(n log n log R), where R is the ratio between the heaviest and the lightest edge in the graph. Our result nearly matches the best known unweighted (2/3+ε₀)-approximation (where ε₀ ∼ 10^{-14} is a small constant) achieved by Assadi and Behnezhad [Assadi and Behnezhad, 2021], and significantly improves upon previous weighted results. Our techniques also extend to the related robust communication model, in which the edges of a graph are partitioned randomly between Alice and Bob. Alice sends a single message of size O(npolylog n) to Bob, who must compute an approximate maximum weight matching. We achieve a (5/6-ε)-approximation using O(n log n log R) words of communication, matching the results of Azarmehr and Behnezhad [Azarmehr and Behnezhad, 2023] for unweighted graphs.
Cite as

Diba Hashemi and Weronika Wrzos-Kaminska. Weighted Matching in the Random-Order Streaming and Robust Communication Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hashemi_et_al:LIPIcs.APPROX/RANDOM.2024.16,
  author =	{Hashemi, Diba and Wrzos-Kaminska, Weronika},
  title =	{{Weighted Matching in the Random-Order Streaming and Robust Communication Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.16},
  URN =		{urn:nbn:de:0030-drops-210097},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.16},
  annote =	{Keywords: Maximum Weight Matching, Streaming, Random-Order Streaming, Robust Communication Complexity}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.43
Interactive Coding with Unbounded Noise

Authors: Eden Fargion, Ran Gelles, and Meghal Gupta

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Interactive coding allows two parties to conduct a distributed computation despite noise corrupting a certain fraction of their communication. Dani et al. (Inf. and Comp., 2018) suggested a novel setting in which the amount of noise is unbounded and can significantly exceed the length of the (noise-free) computation. While no solution is possible in the worst case, under the restriction of oblivious noise, Dani et al. designed a coding scheme that succeeds with a polynomially small failure probability. We revisit the question of conducting computations under this harsh type of noise and devise a computationally-efficient coding scheme that guarantees the success of the computation, except with an exponentially small probability. This higher degree of correctness matches the case of coding schemes with a bounded fraction of noise. Our simulation of an N-bit noise-free computation in the presence of T corruptions, communicates an optimal number of O(N+T) bits and succeeds with probability 1-2^(-Ω(N)). We design this coding scheme by introducing an intermediary noise model, where an oblivious adversary can choose the locations of corruptions in a worst-case manner, but the effect of each corruption is random: the noise either flips the transmission with some probability or otherwise erases it. This randomized abstraction turns out to be instrumental in achieving an optimal coding scheme.
Cite as

Eden Fargion, Ran Gelles, and Meghal Gupta. Interactive Coding with Unbounded Noise. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fargion_et_al:LIPIcs.APPROX/RANDOM.2024.43,
  author =	{Fargion, Eden and Gelles, Ran and Gupta, Meghal},
  title =	{{Interactive Coding with Unbounded Noise}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.43},
  URN =		{urn:nbn:de:0030-drops-210361},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.43},
  annote =	{Keywords: Distributed Computation with Noisy Links, Interactive Coding, Noise Resilience, Unbounded Noise, Random Erasure-Flip Noise}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.57
Stochastic Distance in Property Testing

Authors: Uri Meir, Gregory Schwartzman, and Yuichi Yoshida

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We introduce a novel concept termed "stochastic distance" for property testing. Diverging from the traditional definition of distance, where a distance t implies that there exist t edges that can be added to ensure a graph possesses a certain property (such as k-edge-connectivity), our new notion implies that there is a high probability that adding t random edges will endow the graph with the desired property. While formulating testers based on this new distance proves challenging in a sequential environment, it is much easier in a distributed setting. Taking k-edge-connectivity as a case study, we design ultra-fast testing algorithms in the CONGEST model. Our introduction of stochastic distance offers a more natural fit for the distributed setting, providing a promising avenue for future research in emerging models of computation.
Cite as

Uri Meir, Gregory Schwartzman, and Yuichi Yoshida. Stochastic Distance in Property Testing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 57:1-57:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{meir_et_al:LIPIcs.APPROX/RANDOM.2024.57,
  author =	{Meir, Uri and Schwartzman, Gregory and Yoshida, Yuichi},
  title =	{{Stochastic Distance in Property Testing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{57:1--57:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.57},
  URN =		{urn:nbn:de:0030-drops-210506},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.57},
  annote =	{Keywords: Connectivity, k-edge connectivity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.7
Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.
Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.12
Streaming Matching and Edge Cover in Practice

Authors: S M Ferdous, Alex Pothen, and Mahantesh Halappanavar

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.
Cite as

S M Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming Matching and Edge Cover in Practice. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ferdous_et_al:LIPIcs.SEA.2024.12,
  author =	{Ferdous, S M and Pothen, Alex and Halappanavar, Mahantesh},
  title =	{{Streaming Matching and Edge Cover in Practice}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.12},
  URN =		{urn:nbn:de:0030-drops-203773},
  doi =		{10.4230/LIPIcs.SEA.2024.12},
  annote =	{Keywords: Matching, Edge Cover, Semi-Streaming Algorithm, Parallel Algorithms, Algorithm Engineering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.42
Path-Reporting Distance Oracles with Logarithmic Stretch and Linear Size

Authors: Shiri Chechik and Tianyi Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given an undirected graph G = (V, E, 𝐰) on n vertices with positive edge weights, a distance oracle is a space-efficient data structure that answers pairwise distance queries in fast runtime. The quality of a distance oracle is measured by three parameters: space, query time, and stretch. In a landmark paper by [Thorup and Zwick, 2001], they showed that for any integer parameter k ≥ 1, there exists a distance oracle with size O(kn^{1+1/k}), O(k) query time, and (2k-1)-stretch error on the approximate distances. After that, there has been a line of subsequent improvements which culminated in the optimal trade-off of O(n^{1+1/k}) space, O(1) query time, and (2k-1)-stretch [Chechik, 2015]. However, these line of constructions did not require that the distance oracle is capable of printing an actual path besides an approximate distance estimate, and there has been a performance gap between path-reporting distance oracles and ones that are not path-reporting. It is known that the earliest construction by [Thorup and Zwick, 2001] is path-reporting, but the parameters are worse by a factor of k. In a later construction by [Wulff-Nilsen, 2013], the query time was improved from O(k) to O(log k). Better trade-offs were discovered in [Elkin and Pettie, 2015] where the authors broke the O(kn^{1+1/k}) space barrier and achieved O(n^{1+1/k}log k) space with O(log k) query time, but their stretch was blown up to a polynomial O(k^{log_{4/3}7}); they also gave an alternative choice of O(n^{1+1/k}) space which is optimal, and O(k)-stretch which is also optimal up to a constant factor, but their query time rose exponentially to O(n^ε). In a recent work [Elkin and Shabat, 2023], the authors obtained significant improvements of O(n^{1+1/k}log k) space, O(k)-stretch, and O(log log k) query time, or O(n^{1+1/k}) space, O(klog k)-stretch, and O(log log k) query time. All the above constructions of path-reporting distance oracles share a common barrier; that is, they could not achieve optimal space O(n^{1+1/k}) and stretch O(k) simultaneously within logarithmic query time; for example, in the natural regime where k = ⌈log n⌉, previous distance oracles had to pay an extra factor of log log n either in the space or stretch. As our result, we bypass this barrier by a new construction of path-reporting distance oracles with O(n^{1+1/k}) space and O(k)-stretch and O(log log k) query time.
Cite as

Shiri Chechik and Tianyi Zhang. Path-Reporting Distance Oracles with Logarithmic Stretch and Linear Size. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2024.42,
  author =	{Chechik, Shiri and Zhang, Tianyi},
  title =	{{Path-Reporting Distance Oracles with Logarithmic Stretch and Linear Size}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{42:1--42:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.42},
  URN =		{urn:nbn:de:0030-drops-201859},
  doi =		{10.4230/LIPIcs.ICALP.2024.42},
  annote =	{Keywords: graph algorithms, shortest paths, distance oracles}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.50
Fully-Scalable MPC Algorithms for Clustering in High Dimension

Authors: Artur Czumaj, Guichen Gao, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be n^σ for arbitrarily small fixed σ > 0. Importantly, the local memory may be substantially smaller than the number of clusters k, yet all our algorithms are fast, i.e., run in O(1) rounds. We first devise a fast MPC algorithm for O(1)-approximation of uniform Facility Location. This is the first fully-scalable MPC algorithm that achieves O(1)-approximation for any clustering problem in general geometric setting; previous algorithms only provide poly(log n)-approximation or apply to restricted inputs, like low dimension or small number of clusters k; e.g. [Bhaskara and Wijewardena, ICML'18; Cohen-Addad et al., NeurIPS'21; Cohen-Addad et al., ICML'22]. We then build on this Facility Location result and devise a fast MPC algorithm that achieves O(1)-bicriteria approximation for k-Median and for k-Means, namely, it computes (1+ε)k clusters of cost within O(1/ε²)-factor of the optimum for k clusters. A primary technical tool that we introduce, and may be of independent interest, is a new MPC primitive for geometric aggregation, namely, computing for every data point a statistic of its approximate neighborhood, for statistics like range counting and nearest-neighbor search. Our implementation of this primitive works in high dimension, and is based on consistent hashing (aka sparse partition), a technique that was recently used for streaming algorithms [Czumaj et al., FOCS'22].
Cite as

Artur Czumaj, Guichen Gao, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý. Fully-Scalable MPC Algorithms for Clustering in High Dimension. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2024.50,
  author =	{Czumaj, Artur and Gao, Guichen and Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Vesel\'{y}, Pavel},
  title =	{{Fully-Scalable MPC Algorithms for Clustering in High Dimension}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.50},
  URN =		{urn:nbn:de:0030-drops-201938},
  doi =		{10.4230/LIPIcs.ICALP.2024.50},
  annote =	{Keywords: Massively parallel computing, high dimension, facility location, k-median, k-means}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.65
Optimal Electrical Oblivious Routing on Expanders

Authors: Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper, we investigate the question of whether the electrical flow routing is a good oblivious routing scheme on an m-edge graph G = (V, E) that is a Φ-expander, i.e. where |∂ S| ≥ Φ ⋅ vol(S) for every S ⊆ V, vol(S) ≤ vol(V)/2. Beyond its simplicity and structural importance, this question is well-motivated by the current state-of-the-art of fast algorithms for 𝓁_∞ oblivious routings that reduce to the expander-case which is in turn solved by electrical flow routing. Our main result proves that the electrical routing is an O(Φ^{-1} log m)-competitive oblivious routing in the 𝓁₁- and 𝓁_∞-norms. We further observe that the oblivious routing is O(log² m)-competitive in the 𝓁₂-norm and, in fact, O(log m)-competitive if 𝓁₂-localization is O(log m) which is widely believed. Using these three upper bounds, we can smoothly interpolate to obtain upper bounds for every p ∈ [2, ∞] and q given by 1/p + 1/q = 1. Assuming 𝓁₂-localization in O(log m), we obtain that in 𝓁_p and 𝓁_q, the electrical oblivious routing is O(Φ^{-(1-2/p)}log m) competitive. Using the currently known result for 𝓁₂-localization, this ratio deteriorates by at most a sublogarithmic factor for every p, q ≠ 2. We complement our upper bounds with lower bounds that show that the electrical routing for any such p and q is Ω(Φ^{-(1-2/p)} log m)-competitive. This renders our results in 𝓁₁ and 𝓁_∞ unconditionally tight up to constants, and the result in any 𝓁_p- and 𝓁_q-norm to be tight in case of 𝓁₂-localization in O(log m).
Cite as

Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva. Optimal Electrical Oblivious Routing on Expanders. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{florescu_et_al:LIPIcs.ICALP.2024.65,
  author =	{Florescu, Cella and Kyng, Rasmus and Gutenberg, Maximilian Probst and Sachdeva, Sushant},
  title =	{{Optimal Electrical Oblivious Routing on Expanders}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{65:1--65:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.65},
  URN =		{urn:nbn:de:0030-drops-202083},
  doi =		{10.4230/LIPIcs.ICALP.2024.65},
  annote =	{Keywords: Expanders, Oblivious routing for 𝓁\underlinep, Electrical flow routing}
}
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