9 Search Results for "Shepherd, F. Bruce"

Document
DOI: 10.4230/LIPIcs.DISC.2025.23
Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection

Authors: Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo

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

Abstract
Payment channel networks (PCNs) are a promising technology that alleviates blockchain scalability by shifting the transaction load from the blockchain to the PCN. Nevertheless, the network topology has to be carefully designed to maximise the transaction throughput in PCNs. Additionally, users in PCNs also have to make optimal decisions on which transactions to forward and which to reject to prolong the lifetime of their channels. In this work, we consider an input sequence of transactions over p parties. Each transaction consists of a transaction size, source, and target, and can be either accepted or rejected (entailing a cost). The goal is to design a PCN topology among the p cooperating parties, along with the channel capacities, and then output a decision for each transaction in the sequence to minimise the cost of creating and augmenting channels, as well as the cost of rejecting transactions. Our main contribution is an 𝒪(p) approximation algorithm for the problem with p parties. We further show that with some assumptions on the distribution of transactions, we can reduce the approximation ratio to 𝒪(√p). We complement our theoretical analysis with an empirical study of our assumptions and approach in the context of the Lightning Network.
Cite as

Krishnendu Chatterjee, Jan Matyáš Křišťan, Stefan Schmid, Jakub Svoboda, and Michelle Yeo. Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chatterjee_et_al:LIPIcs.DISC.2025.23,
  author =	{Chatterjee, Krishnendu and K\v{r}i\v{s}\v{t}an, Jan Maty\'{a}\v{s} and Schmid, Stefan and Svoboda, Jakub and Yeo, Michelle},
  title =	{{Boosting Payment Channel Network Liquidity with Topology Optimization and Transaction Selection}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{23:1--23:22},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-248402},
  doi =		{10.4230/LIPIcs.DISC.2025.23},
  annote =	{Keywords: Blockchains, Cryptocurrencies, Payment Channel Networks, Throughput, Optimisation, Graph Algorithms, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.25
Model-Agnostic Approximation of Constrained Forest Problems

Authors: Corinna Coupette, Alipasha Montaseri, and Christoph Lenzen

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

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

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

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@InProceedings{coupette_et_al:LIPIcs.DISC.2025.25,
  author =	{Coupette, Corinna and Montaseri, Alipasha and Lenzen, Christoph},
  title =	{{Model-Agnostic Approximation of Constrained Forest Problems}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{25:1--25:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.25},
  URN =		{urn:nbn:de:0030-drops-248420},
  doi =		{10.4230/LIPIcs.DISC.2025.25},
  annote =	{Keywords: Distributed Graph Algorithms, Model-Agnostic Algorithms, Steiner Forest}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.107
Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts

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

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

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

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

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@InProceedings{haeupler_et_al:LIPIcs.ESA.2025.107,
  author =	{Haeupler, Bernhard and Long, Yaowei and Saranurak, Thatchaphol and Wang, Shengzhe},
  title =	{{Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{107:1--107:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.107},
  URN =		{urn:nbn:de:0030-drops-245765},
  doi =		{10.4230/LIPIcs.ESA.2025.107},
  annote =	{Keywords: Length-Constrained Expander, Expander Decomposition, Shortcut}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.14
Improved Lower Bounds on Multiflow-Multicut Gaps

Authors: Sina Kalantarzadeh and Nikhil Kumar

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

Abstract
Given a set of source-sink pairs, the maximum multiflow problem asks for the maximum total amount of flow that can be feasibly routed between them. The minimum multicut, a dual problem to multiflow, seeks the minimum-cost set of edges whose removal disconnects all the source-sink pairs. It is easy to see that the value of the minimum multicut is at least that of the maximum multiflow, and their ratio is called the multiflow-multicut gap. The classical max-flow min-cut theorem states that when there is only one source-sink pair, the gap is exactly one. However, in general, it is well known that this gap can be arbitrarily large. In this paper, we study this gap for classes of planar graphs and establish improved lower bound results. In particular, we show that this gap is at least 20/9 for the class of planar graphs, improving upon the decades-old lower bound of 2. More importantly, we develop new techniques for proving such a lower bound, which may be useful in other settings as well.
Cite as

Sina Kalantarzadeh and Nikhil Kumar. Improved Lower Bounds on Multiflow-Multicut Gaps. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kalantarzadeh_et_al:LIPIcs.APPROX/RANDOM.2025.14,
  author =	{Kalantarzadeh, Sina and Kumar, Nikhil},
  title =	{{Improved Lower Bounds on Multiflow-Multicut Gaps}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.14},
  URN =		{urn:nbn:de:0030-drops-243803},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.14},
  annote =	{Keywords: Approximation Algorithms, Randomized Algorithms, Linear Programming, Graph Algorithms, Scheduling, Multicut, Multiflow}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.32
Light Edge Fault Tolerant Graph Spanners

Authors: Greg Bodwin, Michael Dinitz, Ama Koranteng, and Lily Wang

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

Abstract
There has recently been significant interest in fault tolerant spanners, which are spanners that still maintain their stretch guarantees after some nodes or edges fail. This work has culminated in an almost complete understanding of the three-way tradeoff between stretch, sparsity, and number of faults tolerated. However, despite some progress in metric settings, there have been no results to date on the tradeoff in general graphs between stretch, lightness, and number of faults tolerated. We initiate the study of light edge fault tolerant (EFT) graph spanners, obtaining the first such results. First, we observe that lightness can be unbounded if we use the traditional definition (normalizing by the MST). We then argue that a natural definition of fault-tolerant lightness is to instead normalize by a min-weight fault tolerant connectivity preserver; essentially, a fault-tolerant version of the MST. However, even with this, we show that it is still not generally possible to construct f-EFT spanners whose weight compares reasonably to the weight of a min-weight f-EFT connectivity preserver. In light of this lower bound, it is natural to then consider bicriteria notions of lightness, where we compare the weight of an f-EFT spanner to a min-weight (f' > f)-EFT connectivity preserver. The most interesting question is to determine the minimum value of f' that allows for reasonable lightness upper bounds. Our main result is a precise answer to this question: f' = 2f. In particular, we show that the lightness can be untenably large (roughly n/k for a k-spanner) if one normalizes by the min-weight (2f-1)-EFT connectivity preserver. But if one normalizes by the min-weight 2f-EFT connectivity preserver, then we show that the lightness is bounded by just O(f^{1/2}) times the non-fault tolerant lightness (roughly n^{1/k} for a (1+ε)(2k-1)-spanner).
Cite as

Greg Bodwin, Michael Dinitz, Ama Koranteng, and Lily Wang. Light Edge Fault Tolerant Graph Spanners. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bodwin_et_al:LIPIcs.ICALP.2025.32,
  author =	{Bodwin, Greg and Dinitz, Michael and Koranteng, Ama and Wang, Lily},
  title =	{{Light Edge Fault Tolerant Graph Spanners}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.32},
  URN =		{urn:nbn:de:0030-drops-234093},
  doi =		{10.4230/LIPIcs.ICALP.2025.32},
  annote =	{Keywords: Fault Tolerant Spanners, Light Spanners}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.90
Revisiting Directed Disjoint Paths on Tournaments (And Relatives)

Authors: Guilherme de C. M. Gomes, Raul Lopes, and Ignasi Sau

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

Abstract
In the Directed Disjoint Paths problem (k-DDP), we are given a digraph and k pairs of terminals, and the goal is to find k pairwise vertex-disjoint paths connecting each pair of terminals. Bang-Jensen and Thomassen [SIAM J. Discrete Math. 1992] claimed that k-DDP is NP-complete on tournaments, and this result triggered a very active line of research about the complexity of the problem on tournaments and natural superclasses. We identify a flaw in their proof, which has been acknowledged by the authors, and provide a new NP-completeness proof. From an algorithmic point of view, Fomin and Pilipczuk [J. Comb. Theory B 2019] provided an FPT algorithm for the edge-disjoint version of the problem on semicomplete digraphs, and showed that their technique cannot work for the vertex-disjoint version. We overcome this obstacle by showing that the version of k-DDP where we allow congestion c on the vertices is FPT on semicomplete digraphs provided that c is greater than k/2. This is based on a quite elaborate irrelevant vertex argument inspired by the edge-disjoint version, and we show that our choice of c is best possible for this technique, with a counterexample with no irrelevant vertices when c ≤ k/2. We also prove that k-DDP on digraphs that can be partitioned into h semicomplete digraphs is W[1]-hard parameterized by k+h, which shows that the XP algorithm presented by Chudnovsky, Scott, and Seymour [J. Comb. Theory B 2019] is essentially optimal.
Cite as

Guilherme de C. M. Gomes, Raul Lopes, and Ignasi Sau. Revisiting Directed Disjoint Paths on Tournaments (And Relatives). In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 90:1-90:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dec.m.gomes_et_al:LIPIcs.ICALP.2025.90,
  author =	{de C. M. Gomes, Guilherme and Lopes, Raul and Sau, Ignasi},
  title =	{{Revisiting Directed Disjoint Paths on Tournaments (And Relatives)}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{90:1--90:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.90},
  URN =		{urn:nbn:de:0030-drops-234678},
  doi =		{10.4230/LIPIcs.ICALP.2025.90},
  annote =	{Keywords: directed graphs, tournaments, semicomplete digraphs, directed disjoint paths, congestion, parameterized complexity, directed pathwidth}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.17
Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths

Authors: Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach

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

Abstract
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) n-vertex graph G along with k terminal pairs (s_1,t_1),(s_2,t_2),…,(s_k,t_k). The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of k. Lochet’s result implies the existence of a polynomial-time ck-approximation for Maximum Vertex-Disjoint Shortest Paths, where c ≤ 1 is a constant. (One can guess 1/c terminal pairs to connect in k^O(1/c) time and then utilize Lochet’s algorithm to compute the solution in n^f(1/c) time.) Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an o(k)-approximation within f(k) ⋅ poly(n) time for any function f that only depends on k. Our second result demonstrates the infeasibility of achieving an approximation ratio of m^{1/2-ε} in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a ⌈√𝓁⌉-approximation, where 𝓁 is the number of edges in all the paths of an optimal solution. Since 𝓁 ≤ n, this underscores the tightness of the m^{1/2-ε}-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by 𝓁 but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.
Cite as

Matthias Bentert, Fedor V. Fomin, and Petr A. Golovach. Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.STACS.2025.17,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A.},
  title =	{{Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.17},
  URN =		{urn:nbn:de:0030-drops-228422},
  doi =		{10.4230/LIPIcs.STACS.2025.17},
  annote =	{Keywords: Inapproximability, Fixed-parameter tractability, Parameterized approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.7
Faster Edge Coloring by Partition Sieving

Authors: Shyan Akmal and Tomohiro Koana

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

Abstract
In the Edge Coloring problem, we are given an undirected graph G with n vertices and m edges, and are tasked with finding the smallest positive integer k so that the edges of G can be assigned k colors in such a way that no two edges incident to the same vertex are assigned the same color. Edge Coloring is a classic NP-hard problem, and so significant research has gone into designing fast exponential-time algorithms for solving Edge Coloring and its variants exactly. Prior work showed that Edge Coloring can be solved in 2^mpoly(n) time and polynomial space, and in graphs with average degree d in 2^{(1-ε_d)m}⋅poly(n) time and exponential space, where ε_d = (1/d)^Θ(d³). We present an algorithm that solves Edge Coloring in 2^{m-3n/5}⋅poly(n) time and polynomial space. Our result is the first algorithm for this problem which simultaneously runs in faster than 2^m⋅poly(m) time and uses only polynomial space. In graphs of average degree d, our algorithm runs in 2^{(1-6/(5d))m}⋅poly(n) time, which has far better dependence in d than previous results. We also consider a generalization of Edge Coloring called List Edge Coloring, where each edge e in the input graph comes with a list L_e ⊆ {1, …, k} of colors, and we must determine whether we can assign each edge a color from its list so that no two edges incident to the same vertex receive the same color. We show that this problem can be solved in 2^{(1-6/(5k))m}⋅poly(n) time and polynomial space. The previous best algorithm for List Edge Coloring took 2^m⋅poly(n) time and space. Our algorithms are algebraic, and work by constructing a special polynomial P based off the input graph that contains a multilinear monomial (i.e., a monomial where every variable has degree at most one) if and only if the answer to the List Edge Coloring problem on the input graph is YES. We then solve the problem by detecting multilinear monomials in P. Previous work also employed such monomial detection techniques to solve Edge Coloring. We obtain faster algorithms both by carefully constructing our polynomial P, and by improving the runtimes for certain structured monomial detection problems using a technique we call partition sieving.
Cite as

Shyan Akmal and Tomohiro Koana. Faster Edge Coloring by Partition Sieving. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.STACS.2025.7,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Faster Edge Coloring by Partition Sieving}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.7},
  URN =		{urn:nbn:de:0030-drops-228328},
  doi =		{10.4230/LIPIcs.STACS.2025.7},
  annote =	{Keywords: Coloring, Edge coloring, Chromatic index, Matroid, Pfaffian, Algebraic algorithm}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.23
Multi-Agent Submodular Optimization

Authors: Richard Santiago and F. Bruce Shepherd

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
Recent years have seen many algorithmic advances in the area of submodular optimization: (SO) min/max~f(S): S in F, where F is a given family of feasible sets over a ground set V and f:2^V - > R is submodular. This progress has been coupled with a wealth of new applications for these models. Our focus is on a more general class of multi-agent submodular optimization (MASO) min/max Sum_{i=1}^{k} f_i(S_i): S_1 u+ S_2 u+ ... u+ S_k in F. Here we use u+ to denote disjoint union and hence this model is attractive where resources are being allocated across k agents, each with its own submodular cost function f_i(). This was introduced in the minimization setting by Goel et al. In this paper we explore the extent to which the approximability of the multi-agent problems are linked to their single-agent versions, referred to informally as the multi-agent gap. We present different reductions that transform a multi-agent problem into a single-agent one. For minimization, we show that (MASO) has an O(alpha * min{k, log^2 (n)})-approximation whenever (SO) admits an alpha-approximation over the convex formulation. In addition, we discuss the class of "bounded blocker" families where there is a provably tight O(log n) multi-agent gap between (MASO) and (SO). For maximization, we show that monotone (resp. nonmonotone) (MASO) admits an alpha (1-1/e) (resp. alpha * 0.385) approximation whenever monotone (resp. nonmonotone) (SO) admits an alpha-approximation over the multilinear formulation; and the 1-1/e multi-agent gap for monotone objectives is tight. We also discuss several families (such as spanning trees, matroids, and p-systems) that have an (optimal) multi-agent gap of 1. These results substantially expand the family of tractable models for submodular maximization.
Cite as

Richard Santiago and F. Bruce Shepherd. Multi-Agent Submodular Optimization. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{santiago_et_al:LIPIcs.APPROX-RANDOM.2018.23,
  author =	{Santiago, Richard and Shepherd, F. Bruce},
  title =	{{Multi-Agent Submodular Optimization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.23},
  URN =		{urn:nbn:de:0030-drops-94276},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.23},
  annote =	{Keywords: submodular optimization, multi-agent, approximation algorithms}
}
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