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DOI: 10.4230/LIPIcs.STACS.2026.53

Maximum Reachability Orientation of Mixed Graphs

Authors: Florian Hörsch

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

Abstract

We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph D, we use P(D) for the set of ordered pairs of distinct vertices in V(D) and we define κ_D:P(D) → {0,1} by κ_D(u,v) = 1 if v is reachable from u in D, and κ_D(u,v) = 0, otherwise. We use R(D) = ∑_{(u,v) ∈ P(D)}κ_D(u,v). Now, given a mixed graph G, we aim to find an orientation x⃑{G} of G that maximizes R(x⃑{G}). Hakimi, Schmeichel, and Young proved that the problem can be solved in polynomial time when restricted to undirected inputs. They inquired about the complexity in mixed graphs. We answer this question by showing that this problem is NP-hard, and, moreover, APX-hard. We then develop a finer understanding of how quickly the problem becomes difficult when going from undirected to mixed graphs. To this end, we consider the parameterized complexity of the problem with respect to the number k of preoriented arcs of G, a poorly studied form of parameterization. We show that the problem can be solved in time n^{O(k)} and that a (1-ε)-approximation can be computed in time f(k,ε)n^{O(1)} for any ε > 0.

Cite as

Florian Hörsch. Maximum Reachability Orientation of Mixed Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 53:1-53:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{horsch:LIPIcs.STACS.2026.53,
  author =	{H\"{o}rsch, Florian},
  title =	{{Maximum Reachability Orientation of Mixed Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{53:1--53:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.53},
  URN =		{urn:nbn:de:0030-drops-255421},
  doi =		{10.4230/LIPIcs.STACS.2026.53},
  annote =	{Keywords: orientations, mixed graphs, reachability, parameterized complexity, approximation}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2025.38

Structural Parameters for Steiner Orientation

Authors: Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract

We consider the Steiner Orientation problem, where we are given as input a mixed graph G = (V,E,A) and a set of k demand pairs (s_i,t_i), i ∈ [k]. The goal is to orient the undirected edges of G in a way that the resulting directed graph has a directed path from s_i to t_i for all i ∈ [k]. We adopt the point of view of structural parameterized complexity and investigate the complexity of Steiner Orientation for standard measures, such as treewidth. Our results indicate that Steiner Orientation is a surprisingly hard problem from this point of view. In particular, our main contributions are the following: 1) We show that Steiner Orientation is NP-complete on instances where the underlying graph has feedback vertex number 2, treewidth 2, pathwidth 3, and vertex integrity 6. 2) We present an XP algorithm parameterized by vertex cover number vc of complexity n^O(vc²). Furthermore, we show that this running time is essentially optimal by proving that a running time of n^o(vc²) would refute the ETH. 3) We consider parameterizations by the number of undirected or directed edges (|E| or |A|) and we observe that the trivial 2^|E| n^O(1)-time algorithm for the former parameter is optimal under the SETH. Complementing this, we show that the problem admits a 2^O(|A|) n^O(1)-time algorithm. In addition to the above, we consider the complexity of Steiner Orientation parameterized by tw+k (FPT), distance to clique (FPT), and vc+k (FPT with a polynomial kernel).

Cite as

Tesshu Hanaka, Michael Lampis, Nikolaos Melissinos, Edouard Nemery, Hirotaka Ono, and Manolis Vasilakis. Structural Parameters for Steiner Orientation. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.ISAAC.2025.38,
  author =	{Hanaka, Tesshu and Lampis, Michael and Melissinos, Nikolaos and Nemery, Edouard and Ono, Hirotaka and Vasilakis, Manolis},
  title =	{{Structural Parameters for Steiner Orientation}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{38:1--38:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.38},
  URN =		{urn:nbn:de:0030-drops-249461},
  doi =		{10.4230/LIPIcs.ISAAC.2025.38},
  annote =	{Keywords: ETH, Steiner Orientation, Treewidth}
}

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

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.115

On the Complexity of Hazard-Free Formulas

Authors: Leah London Arazi and Amir Shpilka

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

Abstract

This paper studies the hazard-free formula complexity of Boolean functions. Our first result shows that unate functions are the only Boolean functions for which the monotone formula complexity of the hazard-derivative equals the hazard-free formula complexity of the function itself. Consequently, they are the only functions for which the hazard-derivative approach of Ikenmeyer et al. (J. ACM, 2019) yields optimal bounds. Our second result proves that the hazard-free formula complexity of a uniformly random Boolean function is at most 2^{(1+o(1))n}. Prior to this, no better upper bound than O(3ⁿ) was known. Notably, unlike in the general case of Boolean circuits and formulas, where the typical complexity is derived from that of the multiplexer function with n-bit selector, the hazard-free formula complexity of a random function is smaller than the optimal hazard-free formula for the multiplexer by an exponential factor in n. We provide two proofs of this fact. The first is direct, bounding the number of prime implicants of a random Boolean function and using this bound to construct a DNF of the claimed size. The second introduces a new and independently interesting result: a weak converse to the hazard-derivative lower bound method, which gives an upper bound on the hazard-free complexity of a function in terms of the monotone complexity of a subset of its hazard-derivatives. Additionally, we explore the hazard-free formula complexity of block composition of Boolean functions and obtain a result in the hazard-free setting that is analogous to a result of Karchmer, Raz, and Wigderson (Computational Complexity, 1995) in the monotone setting. We show that our result implies a stronger lower bound on the hazard-free formula depth of the block composition of the set covering function with the multiplexer function than the bound obtained via the hazard-derivative method.

Cite as

Leah London Arazi and Amir Shpilka. On the Complexity of Hazard-Free Formulas. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 115:1-115:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{londonarazi_et_al:LIPIcs.ICALP.2025.115,
  author =	{London Arazi, Leah and Shpilka, Amir},
  title =	{{On the Complexity of Hazard-Free Formulas}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{115:1--115:19},
  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.2025.115},
  URN =		{urn:nbn:de:0030-drops-234920},
  doi =		{10.4230/LIPIcs.ICALP.2025.115},
  annote =	{Keywords: Hazard-free computation, Boolean formulas, monotone formulas, Karchmer-Wigderson games, communication complexity, lower bounds}
}

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

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.60

Nearly Optimal Local Algorithms for Constructing Sparse Spanners of Clusterable Graphs

Authors: Reut Levi, Moti Medina, and Omer Tubul

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

Abstract

In this paper, we study the problem of locally constructing a sparse spanning subgraph (LSSG), introduced by Levi, Ron, and Rubinfeld (ALGO'20). In this problem, the goal is to locally decide for each e ∈ E if it is in G' where G' is a connected subgraph of G (determined only by G and the randomness of the algorithm). We provide an LSSG that receives as a parameter a lower bound, ϕ, on the conductance of G whose query complexity is Õ(√n/ϕ²). This is almost optimal when ϕ is a constant since Ω(√n) queries are necessary even when G is an expander. Furthermore, this improves the state of the art of Õ(n^{2/3}) queries for ϕ = Ω(1/n^{1/12}). We then extend our result for (k, ϕ_in, ϕ_out)-clusterable graphs and provide an algorithm whose query complexity is Õ(√n + ϕ_out n) for constant k and ϕ_in. This bound is almost optimal when ϕ_out = O(1/√n).

Cite as

Reut Levi, Moti Medina, and Omer Tubul. Nearly Optimal Local Algorithms for Constructing Sparse Spanners of Clusterable Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 60:1-60:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{levi_et_al:LIPIcs.APPROX/RANDOM.2024.60,
  author =	{Levi, Reut and Medina, Moti and Tubul, Omer},
  title =	{{Nearly Optimal Local Algorithms for Constructing Sparse Spanners of Clusterable Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{60:1--60:21},
  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.2024.60},
  URN =		{urn:nbn:de:0030-drops-210537},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.60},
  annote =	{Keywords: Locally Computable Algorithms, Sublinear algorithms, Spanning Subgraphs, Clusterbale Graphs}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2023.19

Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations

Authors: Noy Biton, Reut Levi, and Moti Medina

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract

We study the problem of finding a Hamiltonian cycle under the promise that the input graph has a minimum degree of at least n/2, where n denotes the number of vertices in the graph. The classical theorem of Dirac states that such graphs (a.k.a. Dirac graphs) are Hamiltonian, i.e., contain a Hamiltonian cycle. Moreover, finding a Hamiltonian cycle in Dirac graphs can be done in polynomial time in the classical centralized model. This paper presents a randomized distributed CONGEST algorithm that finds w.h.p. a Hamiltonian cycle (as well as maximum matching) within O(log n) rounds under the promise that the input graph is a Dirac graph. This upper bound is in contrast to general graphs in which both the decision and search variants of Hamiltonicity require Ω̃(n²) rounds, as shown by Bachrach et al. [PODC'19]. In addition, we consider two generalizations of Dirac graphs: Ore graphs and Rahman-Kaykobad graphs [IPL'05]. In Ore graphs, the sum of the degrees of every pair of non-adjacent vertices is at least n, and in Rahman-Kaykobad graphs, the sum of the degrees of every pair of non-adjacent vertices plus their distance is at least n+1. We show how our algorithm for Dirac graphs can be adapted to work for these more general families of graphs.

Cite as

Noy Biton, Reut Levi, and Moti Medina. Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{biton_et_al:LIPIcs.MFCS.2023.19,
  author =	{Biton, Noy and Levi, Reut and Medina, Moti},
  title =	{{Distributed CONGEST Algorithm for Finding Hamiltonian Paths in Dirac Graphs and Generalizations}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.19},
  URN =		{urn:nbn:de:0030-drops-185534},
  doi =		{10.4230/LIPIcs.MFCS.2023.19},
  annote =	{Keywords: the CONGEST model, Hamiltonian Path, Hamiltonian Cycle, Dirac graphs, Ore graphs, graph-algorithms}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2022.32

Small Hazard-Free Transducers

Authors: Johannes Bund, Christoph Lenzen, and Moti Medina

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

Ikenmeyer et al. (JACM'19) proved an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions. This raises the question: which classes of functions permit efficient hazard-free circuits? In this work, we prove that circuit implementations of transducers with small state space are such a class. A transducer is a finite state machine that transcribes, symbol by symbol, an input string of length n into an output string of length n. We present a construction that transforms any function arising from a transducer into an efficient circuit of size 𝒪(n) computing the hazard-free extension of the function. More precisely, given a transducer with s states, receiving n input symbols encoded by l bits, and computing n output symbols encoded by m bits, the transducer has a hazard-free circuit of size n*m*2^{𝒪(s+𝓁)} and depth 𝒪(s*log(n) + 𝓁); in particular, if s, 𝓁,m ∈ 𝒪(1), size and depth are asymptotically optimal. In light of the strong hardness results by Ikenmeyer et al. (JACM'19), we consider this a surprising result.

Cite as

Johannes Bund, Christoph Lenzen, and Moti Medina. Small Hazard-Free Transducers. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 32:1-32:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bund_et_al:LIPIcs.ITCS.2022.32,
  author =	{Bund, Johannes and Lenzen, Christoph and Medina, Moti},
  title =	{{Small Hazard-Free Transducers}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{32:1--32:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.32},
  URN =		{urn:nbn:de:0030-drops-156281},
  doi =		{10.4230/LIPIcs.ITCS.2022.32},
  annote =	{Keywords: Hazard-Freeness, Parallel Prefix Computation, Finite State Transducers}
}

Document

RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.19

Distributed Testing of Graph Isomorphism in the CONGEST Model

Authors: Reut Levi and Moti Medina

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract

In this paper we study the problem of testing graph isomorphism (GI) in the CONGEST distributed model. In this setting we test whether the distributive network, G_U, is isomorphic to G_K which is given as an input to all the nodes in the network, or alternatively, only to a single node. We first consider the decision variant of the problem in which the algorithm should distinguish the case where G_U and G_K are isomorphic from the case where G_U and G_K are not isomorphic. Specifically, if G_U and G_K are not isomorphic then w.h.p. at least one node should output reject and otherwise all nodes should output accept . We provide a randomized algorithm with O(n) rounds for the setting in which G_K is given only to a single node. We prove that for this setting the number of rounds of any deterministic algorithm is Ω̃(n²) rounds, where n denotes the number of nodes, which implies a separation between the randomized and the deterministic complexities of deciding GI . Our algorithm can be adapted to the semi-streaming model, where a single pass is performed and Õ(n) bits of space are used. We then consider the property testing variant of the problem, where the algorithm is only required to distinguish the case that G_U and G_K are isomorphic from the case that G_U and G_K are far from being isomorphic (according to some predetermined distance measure). We show that every (possibly randomized) algorithm, requires Ω(D) rounds, where D denotes the diameter of the network. This lower bound holds even if all the nodes are given G_K as an input, and even if the message size is unbounded. We provide a randomized algorithm with an almost matching round complexity of O(D+(ε^{-1}log n)²) rounds that is suitable for dense graphs (namely, graphs with Ω(n²) edges). We also show that with the same number of rounds it is possible that each node outputs its mapping according to a bijection which is an approximate isomorphism. We conclude with simple simulation arguments that allow us to adapt centralized property testing algorithms and obtain essentially tight algorithms with round complexity Õ(D) for special families of sparse graphs.

Cite as

Reut Levi and Moti Medina. Distributed Testing of Graph Isomorphism in the CONGEST Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{levi_et_al:LIPIcs.APPROX/RANDOM.2020.19,
  author =	{Levi, Reut and Medina, Moti},
  title =	{{Distributed Testing of Graph Isomorphism in the CONGEST Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.19},
  URN =		{urn:nbn:de:0030-drops-126221},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.19},
  annote =	{Keywords: the CONGEST model, graph isomorphism, distributed property testing, distributed decision, graph algorithms}
}

Document

DOI: 10.4230/LIPIcs.DISC.2018.22

Distributed Set Cover Approximation: Primal-Dual with Optimal Locality

Authors: Guy Even, Mohsen Ghaffari, and Moti Medina

Published in: LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

Abstract

This paper presents a deterministic distributed algorithm for computing an f(1+epsilon) approximation of the well-studied minimum set cover problem, for any constant epsilon>0, in O(log (f Delta)/log log (f Delta)) rounds. Here, f denotes the maximum element frequency and Delta denotes the cardinality of the largest set. This f(1+epsilon) approximation almost matches the f-approximation guarantee of standard centralized primal-dual algorithms, which is known to be essentially the best possible approximation for polynomial-time computations. The round complexity almost matches the Omega(log (Delta)/log log (Delta)) lower bound of Kuhn, Moscibroda, Wattenhofer [JACM'16], which holds for even f=2 and for any poly(log Delta) approximation. Our algorithm also gives an alternative way to reproduce the time-optimal 2(1+epsilon)-approximation of vertex cover, with round complexity O(log Delta/log log Delta), as presented by Bar-Yehuda, Censor-Hillel, and Schwartzman [PODC'17] for weighted vertex cover. Our method is quite different and it can be viewed as a locality-optimal way of performing primal-dual for the more general case of set cover. We note that the vertex cover algorithm of Bar-Yehuda et al. does not extend to set cover (when f >= 3).

Cite as

Guy Even, Mohsen Ghaffari, and Moti Medina. Distributed Set Cover Approximation: Primal-Dual with Optimal Locality. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{even_et_al:LIPIcs.DISC.2018.22,
  author =	{Even, Guy and Ghaffari, Mohsen and Medina, Moti},
  title =	{{Distributed Set Cover Approximation: Primal-Dual with Optimal Locality}},
  booktitle =	{32nd International Symposium on Distributed Computing (DISC 2018)},
  pages =	{22:1--22:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Schmid, Ulrich and Widder, Josef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.22},
  URN =		{urn:nbn:de:0030-drops-98114},
  doi =		{10.4230/LIPIcs.DISC.2018.22},
  annote =	{Keywords: Distributed Algorithms, Approximation Algorithms, Set Cover, Vertex Cover}
}

Document

DOI: 10.4230/LIPIcs.DISC.2017.15

Three Notes on Distributed Property Testing

Authors: Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract

In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P. We present a series of results, including: - Testing H-freeness in O(1/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small. - A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time. - For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1/2-1/(s-2)) epsilon^(-1/2-1/(s-2))) rounds, where m is the number of edges in the network graph. - We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)/epsilon)+f((log n)/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. These protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016].

Cite as

Guy Even, Orr Fischer, Pierre Fraigniaud, Tzlil Gonen, Reut Levi, Moti Medina, Pedro Montealegre, Dennis Olivetti, Rotem Oshman, Ivan Rapaport, and Ioan Todinca. Three Notes on Distributed Property Testing. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 15:1-15:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{even_et_al:LIPIcs.DISC.2017.15,
  author =	{Even, Guy and Fischer, Orr and Fraigniaud, Pierre and Gonen, Tzlil and Levi, Reut and Medina, Moti and Montealegre, Pedro and Olivetti, Dennis and Oshman, Rotem and Rapaport, Ivan and Todinca, Ioan},
  title =	{{Three Notes on Distributed Property Testing}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{15:1--15:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.15},
  URN =		{urn:nbn:de:0030-drops-79847},
  doi =		{10.4230/LIPIcs.DISC.2017.15},
  annote =	{Keywords: Property testing, Property correcting, Distributed algorithms, CONGEST model}
}

Document

DOI: 10.4230/LIPIcs.ICALP.2017.6

Sublinear Random Access Generators for Preferential Attachment Graphs

Authors: Guy Even, Reut Levi, Moti Medina, and Adi Rosén

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space and randomness complexities of such samplers. In the standard approach, the whole graph is chosen randomly according to the randomized evolving process, stored in full, and then queries on the sampled graph are answered by simply accessing the stored graph. This may require prohibitive amounts of time, space and random bits, especially when only a small number of queries are actually issued. Instead, we propose to generate the graph on-the-fly, in response to queries, and therefore to require amounts of time, space, and random bits which are a function of the actual number of queries. We focus on two random graph models: the Barabási-Albert Preferential Attachment model (BA-graphs) and the random recursive tree model. We give on-the-fly generation algorithms for both models. With probability 1-1/poly(n), each and every query is answered in polylog(n) time, and the increase in space and the number of random bits consumed by any single query are both polylog(n), where n denotes the number of vertices in the graph. Our results show that, although the BA random graph model is defined by a sequential process, efficient random access to the graph's nodes is possible. In addition to the conceptual contribution, efficient on-the-fly generation of random graphs can serve as a tool for the efficient simulation of sublinear algorithms over large BA-graphs, and the efficient estimation of their performance on such graphs.

Cite as

Guy Even, Reut Levi, Moti Medina, and Adi Rosén. Sublinear Random Access Generators for Preferential Attachment Graphs. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{even_et_al:LIPIcs.ICALP.2017.6,
  author =	{Even, Guy and Levi, Reut and Medina, Moti and Ros\'{e}n, Adi},
  title =	{{Sublinear Random Access Generators for Preferential Attachment Graphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.6},
  URN =		{urn:nbn:de:0030-drops-74242},
  doi =		{10.4230/LIPIcs.ICALP.2017.6},
  annote =	{Keywords: local computation algorithms, preferential attachment graphs, random recursive trees, sublinear algorithms}
}

Document

DOI: 10.4230/LIPIcs.ESA.2016.40

A Constant Approximation Algorithm for Scheduling Packets on Line Networks

Authors: Guy Even, Moti Medina, and Adi Rosén

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract

In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers with the aim of maximizing the throughput. Each node in the network has a local buffer of bounded size B, and each edge (or link) can transmit a limited number c of packets in every time unit. The input to the problem consists of a set of packet requests, each defined by a source node, a destination node, and a release time. We denote by n the size of the network. A solution for this problem is a schedule that delivers (some of the) packets to their destinations without violating the capacity constraints of the network (buffers or edges). Our goal is to design an efficient algorithm that computes a schedule that maximizes the number of packets that arrive to their respective destinations. We give a randomized approximation algorithm with constant approximation ratio for the case where the buffer-size to link-capacity ratio, B/c, does not depend on the input size. This improves over the previously best result of O(log^* n) [Räcke and Rosén SPAA 2009]. Our improvement is based on a new combinatorial lemma that we prove, stating, roughly speaking, that if packets are allowed to stay put in buffers only a limited number of time steps, 2d, where d is the longest source-destination distance, then the optimal solution is decreased by only a constant factor. This claim was not previously known in the integral (unsplitable, zero-one) case, and may find additional applications for routing and scheduling algorithms. While we are not able to give the same improvement for the related problem when packets have hard deadlines, our algorithm does support "soft deadlines". That is, if packets have deadlines, we achieve a constant approximation ratio when the produced solution is allowed to miss deadlines by at most log n time units.

Cite as

Guy Even, Moti Medina, and Adi Rosén. A Constant Approximation Algorithm for Scheduling Packets on Line Networks. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{even_et_al:LIPIcs.ESA.2016.40,
  author =	{Even, Guy and Medina, Moti and Ros\'{e}n, Adi},
  title =	{{A Constant Approximation Algorithm for Scheduling Packets on Line Networks}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.40},
  URN =		{urn:nbn:de:0030-drops-63524},
  doi =		{10.4230/LIPIcs.ESA.2016.40},
  annote =	{Keywords: approximation algorithms, linear programming, randomized rounding, packet scheduling, admission control}
}

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