arXiv subjects

Fabien Dufoulon

Publications and source records attributed to Fabien Dufoulon.

16 recordsLinked to original sources

arXiv2026

Tight Energy Lower Bounds for Distributed Graph Algorithms

There has been a significant recent interest in designing distributed algorithms in the SLEEPING model that minimize the {energy (a.k.a awake) complexity, which measures the number of rounds a node is awake during the algorithm. A node spends non-trivial resources (messages, energy, etc.) only when it is awake and not while sleeping. Energy complexity has been studied for various fundamental problems with respect to minimizing the maximum (worst-case) or the average number of rounds a node is awake. It has been shown that the energy complexities of several fundamental problems such as leader election (LE), broadcast, Minimum Spanning Tree (MST), Maximal Independent Set (MIS) is exponentially smaller compared to their respective best-possible round complexities in the standard CONGEST model (where nodes can only send messages of small size). This raises a fundamental question of whether such significant energy gains are possible for many other fundamental problems. Our main contribution is a general and powerful technique for showing energy lower bounds using information theory. It gives almost a "plug-in" way to show energy lower bounds for various problems in the standard CONGEST model. Our information-theoretic technique allows us to leverage known lower bounds on communication complexity to obtain new, almost optimal (up to logarithmic factors) polynomial (in $n$) lower bounds on energy complexity --- for both worst-case and average-case --- for fundamental graph problems such as triangle enumeration, All-Pairs Shortest Paths (APSP), diameter computation, minimum weight cycle, Maximum Independent Set (MaxIS), Minimum Dominating Set (MinDS), Minimum Vertex Cover (MinVC). The energy lower bounds of these problems match their respective round lower bounds, implying that one cannot obtain any significant gains in energy complexity.

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arXiv2026

Fast Gossip-based Rumor Spreading using Small Messages

We study gossip algorithms for the fundamental rumor spreading problem, where the goal is to disseminate a rumor from a given source node to all nodes in an arbitrary (and unknown) graph. Gossip algorithms allow each node to call only one neighbor per round and are therefore highly message-efficient, with low per-node communication overhead per round. The state of the art present fast gossip algorithms, however they typically leverage large-sized messages. This undermines the light-weight communication advantage of gossip, since even though only one neighbor is contacted per round, the message size can be linear in $n$, the network size. Hence, a fundamental question is whether one can perform fast gossip using small messages. The main contribution of this paper is to answer the above question in the affirmative and present two gossip algorithms that achieve fast rumor spreading using messages of polylog{n} size. Specifically, we present the following algorithms: 1. An algorithm that runs in $O(c \log n / Φ_c)$ rounds for every $c \geq 1$, and $Φ_c$ is the weak conductance. Our bound in terms of weak conductance is essentially optimal. 2. An algorithm that depends on the network diameter (and is independent of the graph's conductance), which runs in $\tilde{O}(D+\sqrt{n})$ rounds with high probability. Our algorithm can be modified to output a minimum spanning tree (MST) in the same number of rounds, which is essentially round-optimal (even for non-gossip algorithms). Our gossip algorithms use graph sketches [Ahn, Guha, McGregor, SODA 2012] in a novel way to overcome communication bottlenecks and achieve small communication overhead with small message sizes.

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arXiv2026

Tight Communication Bounds for Distributed Algorithms in the Quantum Routing Model

We present new distributed quantum algorithms for fundamental distributed computing problems, namely, leader election, broadcast, Minimum Spanning Tree (MST), and Breadth-First Search (BFS) tree, in arbitrary networks. These algorithms are (essentially) optimal with respect to their communication (message) complexity in the {\em quantum routing model} introduced in [PODC 2025]. The message complexity of our algorithms is $\tilde{O}(n)$ for leader election, broadcast, and MST, and $\tilde{O}(\sqrt{mn})$ for BFS ($n$ and $m$ are the number of nodes and edges of the network, respectively). These message bounds are nearly tight in the quantum routing model since we show almost matching corresponding quantum message lower bounds. Our results significantly improve on the prior work of [PODC 2025], who presented distributed quantum algorithms under the same model that had a message complexity of $\tilde{O}(\sqrt{mn})$ for leader election. Our algorithms demonstrate the significant communication advantage that quantum routing has over classical in distributed computing, since $Ω(m)$ is a well-established classical message lower bound for leader election, broadcast, MST, and BFS that applies even to randomized Monte-Carlo algorithms [JACM 2015]. Thus, our quantum algorithms can, in general, give a quadratic advantage in the communication cost for these fundamental problems. A main technical tool we use to design our distributed algorithms is quantum walks based on electric networks. We posit a framework for using quantum walks in the distributed setting to design communication-efficient distributed quantum algorithms. Our framework can be used as a black box to significantly reduce communication costs and may be of independent interest. Additionally, our lower-bound technique for establishing distributed quantum message lower bounds can also be applied to other problems.

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arXiv2025

Energy-Efficient Maximal Independent Sets in Radio Networks

The maximal independent set (MIS) is one of the most fundamental problems in distributed computing, and it has been studied intensively for over four decades. This paper focuses on the MIS problem in the Radio Network model, a standard model widely used to model wireless networks, particularly ad hoc wireless and sensor networks. Energy is a premium resource in these networks, which are typically battery-powered. Hence, designing distributed algorithms that use as little energy as possible is crucial. We use the well-established energy model where a node can be sleeping or awake in a round, and only the awake rounds (when it can send or listen) determine the energy complexity of the algorithm, which we want to minimize. We present new, more energy-efficient MIS algorithms in radio networks with arbitrary and unknown graph topology. We present algorithms for two popular variants of the radio model -- with collision detection (CD) and without collision detection (no-CD). Specifically, we obtain the following results: 1. CD model: We present a randomized distributed MIS algorithm with energy complexity $O(\log n)$, round complexity $O(\log^2 n)$, and failure probability $1 / poly(n)$, where $n$ is the network size. We show that our energy complexity is optimal by showing a matching $Ω(\log n)$ lower bound. 2. no-CD model: In the more challenging no-CD model, we present a randomized distributed MIS algorithm with energy complexity $O(\log^2n \log \log n)$, round complexity $O(\log^3 n \log Δ)$, and failure probability $1 / poly(n)$. The energy complexity of our algorithm is significantly lower than the round (and energy) complexity of $O(\log^3 n)$ of the best known distributed MIS algorithm of Davies [PODC 2023] for arbitrary graph topology.

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arXiv2025

Improved Byzantine Agreement under an Adaptive Adversary

Byzantine agreement is a fundamental problem in fault-tolerant distributed computing that has been studied intensively for the last four decades. Much of the research has focused on a static Byzantine adversary, where the adversary is constrained to choose the Byzantine nodes in advance of the protocol's execution. This work focuses on the harder case of an adaptive Byzantine adversary that can choose the Byzantine nodes \emph{adaptively} based on the protocol's execution. While efficient $O(\log n)$-round protocols ($n$ is the total number of nodes) are known for the static adversary (Goldwasser, Pavlov, and Vaikuntanathan, FOCS 2006) tolerating up to $t < n/(3+ε)$ Byzantine nodes, $Ω(t/\sqrt{n \log n})$ rounds is a well-known lower bound for adaptive adversary [Bar-Joseph and Ben-Or, PODC 1998]. The best-known protocol for adaptive adversary runs in $O(t/\log n)$ rounds [Chor and Coan, IEEE Trans. Soft. Engg., 1985]. This work presents a synchronous randomized Byzantine agreement protocol under an adaptive adversary that improves over previous results. Our protocol works under the powerful \emph{adaptive rushing adversary in the full information model}. That is, we assume that the Byzantine nodes can behave arbitrarily and maliciously, have knowledge about the entire state of the network at every round, including random choices made by all the nodes up to and including the current round, have unlimited computational power, and may collude among themselves. Furthermore, the adversary can \emph{adaptively} corrupt up to $t < n/3$ nodes based on the protocol's execution. We present a simple randomized Byzantine agreement protocol that runs in $O(\min\{t^2\log n/n, t/\log n\})$ rounds that improves over the long-standing bound of $O(t/\log n)$ rounds due to Chor and Coan [IEEE Trans. Soft. Engg., 1985].

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arXiv2025

Message Optimality and Message-Time Trade-offs for APSP and Beyond

Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite limited. To illustrate, for many fundamental distributed graph optimization problems such as (exact) diameter computation, All-Pairs Shortest Paths (APSP), Maximum Matching etc., while (near) round-optimal algorithms are known, message-optimal algorithms are hitherto unknown. More importantly, the existing round-optimal algorithms are not message-optimal. This raises two important questions: (1) Can we design message-optimal algorithms for these problems? (2) Can we give message-time tradeoffs for these problems in case the message-optimal algorithms are not round-optimal? In this work, we focus on a fundamental graph optimization problem, \emph{All Pairs Shortest Path (APSP)}, whose message complexity is still unresolved. We present two main results in the CONGEST model: (1) We give a message-optimal (up to logarithmic factors) algorithm that solves weighted APSP, using $\tilde{O}(n^2)$ messages. This algorithm takes $\tilde{O}(n^2)$ rounds. (2) For any $0 \leq \varepsilon \le 1$, we show how to solve unweighted APSP in $\tilde{O}(n^{2-\varepsilon })$ rounds and $\tilde{O}(n^{2+\varepsilon })$ messages. At one end of this smooth trade-off, we obtain a (nearly) message-optimal algorithm using $\tilde{O}(n^2)$ messages (for $\varepsilon = 0$), whereas at the other end we get a (nearly) round-optimal algorithm using $\tilde{O}(n)$ rounds (for $\varepsilon = 1$). This is the first such message-time trade-off result known.

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arXiv2025

Quantum Communication Advantage for Leader Election and Agreement

This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum communication gives an advantage for both problems by presenting quantum distributed algorithms that significantly outperform their respective classical counterparts under various network topologies. While prior works have studied and analyzed quantum distributed algorithms in the context of (improving) round complexity, a key conceptual contribution of our work is positing a framework to design and analyze the message complexity of quantum distributed algorithms. We present and show how quantum algorithmic techniques such as Grover search, quantum counting, and quantum walks can make distributed algorithms significantly message-efficient. In particular, our leader election protocol for diameter-2 networks uses quantum walks to achieve the improved message complexity. To the best of our knowledge, this is the first such application of quantum walks in distributed computing.

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arXiv2024

The Singular Optimality of Distributed Computation in LOCAL

It has been shown that one can design distributed algorithms that are (nearly) singularly optimal, meaning they simultaneously achieve optimal time and message complexity (within polylogarithmic factors), for several fundamental global problems such as broadcast, leader election, and spanning tree construction, under the $\text{KT}_0$ assumption. With this assumption, nodes have initial knowledge only of themselves, not their neighbors. In this case the time and message lower bounds are $Ω(D)$ and $Ω(m)$, respectively, where $D$ is the diameter of the network and $m$ is the number of edges, and there exist (even) deterministic algorithms that simultaneously match these bounds. On the other hand, under the $\text{KT}_1$ assumption, whereby each node has initial knowledge of itself and the identifiers of its neighbors, the situation is not clear. For the $\text{KT}_1$ CONGEST model (where messages are of small size), King, Kutten, and Thorup (KKT) showed that one can solve several fundamental global problems (with the notable exception of BFS tree construction) such as broadcast, leader election, and spanning tree construction with $\tilde{O}(n)$ message complexity ($n$ is the network size), which can be significantly smaller than $m$. Randomization is crucial in obtaining this result. While the message complexity of the KKT result is near-optimal, its time complexity is $\tilde{O}(n)$ rounds, which is far from the standard lower bound of $Ω(D)$. In this paper, we show that in the $\text{KT}_1$ LOCAL model (where message sizes are not restricted), singular optimality is achievable. Our main result is that all global problems, including BFS tree construction, can be solved in $\tilde{O}(D)$ rounds and $\tilde{O}(n)$ messages, where both bounds are optimal up to polylogarithmic factors. Moreover, we show that this can be achieved deterministically.

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arXiv2024

Fully-Distributed Byzantine Agreement in Sparse Networks

Byzantine agreement is a fundamental problem in fault-tolerant distributed networks that has been studied intensively for the last four decades. Most of these works designed protocols for complete networks. A key goal in Byzantine protocols is to tolerate as many Byzantine nodes as possible. The work of Dwork, Peleg, Pippenger, and Upfal [STOC 1986, SICOMP 1988] was the first to address the Byzantine agreement problem in sparse, bounded degree networks and presented a protocol that achieved almost-everywhere agreement among honest nodes. In such networks, all known Byzantine agreement protocols (e.g., Dwork, Peleg, Pippenger, and Upfal, STOC 1986; Upfal, PODC 1992; King, Saia, Sanwalani, and Vee, FOCS 2006) that tolerated a large number of Byzantine nodes had a major drawback that they were not fully-distributed -- in those protocols, nodes are required to have initial knowledge of the entire network topology. This drawback makes such protocols inapplicable to real-world communication networks such as peer-to-peer (P2P) networks, which are typically sparse and bounded degree and where nodes initially have only local knowledge of themselves and their neighbors. Indeed, a fundamental open question raised by the above works is whether one can design Byzantine protocols that tolerate a large number of Byzantine nodes in sparse networks that work with only local knowledge, i.e., fully-distributed protocols. The work of Augustine, Pandurangan, and Robinson [PODC 2013] presented the first fully-distributed Byzantine agreement protocol that works in sparse networks, but it tolerated only up to $O(\sqrt{n}/ polylog(n))$ Byzantine nodes (where $n$ is the total network size). We answer the earlier open question by presenting fully-distributed Byzantine agreement protocols for sparse, bounded degree networks that tolerate significantly more Byzantine nodes -- up to $O(n/ polylog(n))$ of them.

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arXiv2024

Distributed Coloring in the SLEEPING Model

In distributed network computing, a variant of the LOCAL model has been recently introduced, referred to as the SLEEPING model. In this model, nodes have the ability to decide on which round they are awake, and on which round they are sleeping. Two (adjacent) nodes can exchange messages in a round only if both of them are awake in that round. The SLEEPING model captures the ability of nodes to save energy when they are sleeping. In this framework, a major question is the following: is it possible to design algorithms that are energy efficient, i.e., where each node is awake for a few number of rounds only, without losing too much on the time efficiency, i.e., on the total number of rounds? This paper answers positively to this question, for one of the most fundamental problems in distributed network computing, namely $(Δ+1)$-coloring networks of maximum degree $Δ$. We provide a randomized algorithm with average awake-complexity constant, maximum awake-complexity $O(\log\log n)$ in $n$-node networks, and round-complexity $poly\!\log n$.

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arXiv2023

Distributed MIS in $O(\log\log{n} )$ Awake Complexity

Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best-known (randomized) MIS algorithms have $O(\log{n})$ round complexity on general graphs [Luby, STOC 1986] (where $n$ is the number of nodes), while the best-known lower bound is $Ω(\sqrt{\log{n}/\log\log{n}})$ [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the $O(\log{n})$ round complexity upper bound or showing stronger lower bounds have been longstanding open problems. Our main contribution is to show that MIS can be computed in awake complexity that is exponentially better compared to the best known round complexity of $O(\log n)$ and also bypassing its fundamental $Ω(\sqrt{\log{n}/\log\log{n}})$ round complexity lower bound exponentially. Specifically, we show that MIS can be computed by a randomized distributed (Monte Carlo) algorithm in $O(\log\log{n} )$ awake complexity with high probability (i.e., with probability at least $1 - n^{-1}$). This algorithm has a round complexity of $O((\log^7 n) \log \log n)$. We also show that we can improve the round complexity at the cost of a slight increase in awake complexity, by presenting a randomized distributed (Monte Carlo) algorithm for MIS that, with high probability, computes an MIS in $O((\log\log{n})\log^*n)$ awake complexity and $O((\log^3 n) (\log \log n) \log^*n)$ round complexity. Our algorithms work in the CONGEST model where messages of size $O(\log n)$ bits can be sent per edge per round.

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arXiv2023

Time- and Communication-Efficient Overlay Network Construction via Gossip

We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it knows. The network is assumed to be reconfigurable, i.e., a node can add new connections (edges) to other nodes whose identifier it knows or drop existing connections. Each node initially has only knowledge of its own identifier and the identifiers of its neighbors. The overlay construction problem is, given an arbitrary (connected) graph, to reconfigure it to obtain a bounded-degree expander graph as efficiently as possible. The overlay construction problem is relevant to building real-world peer-to-peer network topologies that have desirable properties such as low diameter, high conductance, robustness to adversarial deletions, etc. Our main result is that we show that starting from any arbitrary (connected) graph $G$ on $n$ nodes and $m$ edges, we can construct an overlay network that is a constant-degree expander in polylog $n$ rounds using only $\tilde{O}(n)$ messages. Our time and message bounds are both essentially optimal (up to polylogarithmic factors). Our distributed overlay construction protocol is very lightweight as it uses gossip (each node communicates with only one neighbor in each round) and also scalable as it uses only $\tilde{O}(n)$ messages, which is sublinear in $m$ (even when $m$ is moderately dense). To the best of our knowledge, this is the first result that achieves overlay network construction in polylog $n$ rounds and $o(m)$ messages. Our protocol uses graph sketches in a novel way to construct an expander overlay that is both time and communication efficient. A consequence of our overlay construction protocol is that distributed computation can be performed very efficiently in this model.

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arXiv2023

The Message Complexity of Distributed Graph Optimization

The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization problems. We focus on four classical graph optimization problems: Maximum Matching (MaxM), Minimum Vertex Cover (MVC), Minimum Dominating Set (MDS), and Maximum Independent Set (MaxIS). In the sequential setting, these problems are representative of a wide spectrum of hardness of approximation. While there has been some progress in understanding the round complexity of distributed algorithms (for both exact and approximate versions) for these problems, much less is known about their message complexity and its relation with the quality of approximation. We almost fully quantify the message complexity of distributed graph optimization by showing the following results...[see paper for full abstract]

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arXiv2023

Beeping Shortest Paths via Hypergraph Bipartite Decomposition

Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in $O (D \log\log n + \log^3 n)$ rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in $O (D \log^2 n + \log^3 n)$ rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the (polynomially-large) hyperedge set of a hypergraph $H = (V_H, E_H)$ into $k = Θ(\log^2 n)$ disjoint subsets $F_1 \cup \cdots \cup F_k = E_H$ such that the (sub-)hypergraph $(V_H, F_i)$ is bipartite in the sense that there exists a vertex subset $U \subseteq V$ such that $|U \cap e| = 1$ for every $e \in F_i$. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.

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arXiv2022

An Almost Singularly Optimal Asynchronous Distributed MST Algorithm

A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental distributed computing problems such as leader election [Kutten et al., JACM 2015] and Minimum Spanning Tree (MST) construction [Pandurangan et al., STOC 2017, Elkin, PODC 2017]. However, it is open whether a singularly (near) optimal bound can be obtained for the MST construction problem in general \emph{asynchronous} CONGEST networks. We present a randomized distributed MST algorithm that, with high probability, computes an MST in \emph{asynchronous} CONGEST networks and takes $\tilde{O}(D^{1+ε} + \sqrt{n})$ time and $\tilde{O}(m)$ messages, where $n$ is the number of nodes, $m$ the number of edges, $D$ is the diameter of the network, and $ε>0$ is an arbitrarily small constant (both time and message bounds hold with high probability). Our algorithm is message optimal (up to a polylog$(n)$ factor) and almost time optimal (except for a $D^ε$ factor). Our result answers an open question raised in Mashregi and King [DISC 2019] by giving the first known asynchronous MST algorithm that has sublinear time (for all $D = O(n^{1-ε})$) and uses $\tilde{O}(m)$ messages. Using a result of Mashregi and King [DISC 2019], this also yields the first asynchronous MST algorithm that is sublinear in both time and messages in the $KT_1$ CONGEST model. A key tool in our algorithm is the construction of a low diameter rooted spanning tree in asynchronous CONGEST that has depth $\tilde{O}(D^{1+ε})$ (for an arbitrarily small constant $ε> 0$) in $\tilde{O}(D^{1+ε})$ time and $\tilde{O}(m)$ messages. To the best of our knowledge, this is the first such construction that is almost singularly optimal in the asynchronous setting.

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arXiv2021

Efficient Deterministic Leader Election for Programmable Matter

It was suggested that a programmable matter system (composed of multiple computationally weak mobile particles) should remain connected at all times since otherwise, reconnection is difficult and may be impossible. At the same time, it was not clear that allowing the system to disconnect carried a significant advantage in terms of time complexity. We demonstrate for a fundamental task, that of leader election, an algorithm where the system disconnects and then reconnects automatically in a non-trivial way (particles can move far away from their former neighbors and later reconnect to others). Moreover, the runtime of the temporarily disconnecting deterministic leader election algorithm is linear in the diameter. Hence, the disconnecting -- reconnecting algorithm is as fast as previous randomized algorithms. When comparing to previous deterministic algorithms, we note that some of the previous work assumed weaker schedulers. Still, the runtime of all the previous deterministic algorithms that did not assume special shapes of the particle system (shapes with no holes) was at least quadratic in $n$, where $n$ is the number of particles in the system. (Moreover, the new algorithm is even faster in some parameters than the deterministic algorithms that did assume special initial shapes.) Since leader election is an important module in algorithms for various other tasks, the presented algorithm can be useful for speeding up other algorithms under the assumption of a strong scheduler. This leaves open the question: "can a deterministic algorithm be as fast as the randomized ones also under weaker schedulers?"

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