arXiv subjects

Yi-Jun Chang

Publications and source records attributed to Yi-Jun Chang.

At least 19 recordsLinked to original sources

arXiv2026

Introvert Clustering for Distributed Graph Algorithms

We introduce a graph decomposition primitive called introvert clustering, which strengthens standard low-diameter clustering by guaranteeing that every clustered vertex keeps at least a $\left(\frac12-\varepsilon\right)$-fraction of its relevant neighbors in its own cluster. Repeatedly applying this primitive yields a layered introvert network decomposition with $O(\log n)$ layers and weak diameter $O(\log n)$. We give two applications in the $\mathsf{LOCAL}$ model. For every constant $\varepsilon>0$, we obtain a $\widetilde O(\log^2 n)$-round deterministic algorithm for list $\left(\frac32+\varepsilon\right)\Delta$-edge coloring on graphs of maximum degree $\Delta\geq\Delta_0(\varepsilon)$; for bipartite graphs, the result holds for all $\Delta$. For every constant $0<\varepsilon<1/4$, we also obtain a $\widetilde O(\log^2 n)$-round deterministic algorithm for a $\left(\frac14-\varepsilon\right)$-locally balanced cut, where every vertex has at least a $\left(\frac14-\varepsilon\right)$-fraction of its neighbors on the opposite side. The resulting algorithms are remarkably simple: edge coloring processes the layers in reverse order and colors each cluster, while locally balanced cut processes them forward and computes a locally maximum cut within each cluster. The introvert guarantee enables these procedures beyond the usual greedy regime of network decomposition. We construct the decomposition in $O(\log^2 n)$ randomized rounds using Miller--Peng--Xu low-diameter clustering and a simple trimming procedure, and deterministically in $\widetilde O(\log^2 n)$ rounds via a white-box adaptation of the recursive network decomposition algorithm of Ghaffari and Grunau [FOCS 2024].

cs.DC↗

arXiv2026

A Few Shared Random Bits Suffice for Constant-Round Almost Stable Matching

We show that almost stable matching can be solved in constant distributed rounds on general bipartite graphs $G=(V,E)$ using only a few shared random bits. Specifically, in the $\congest$ model, we compute a matching whose expected number of blocking pairs is at most $\varepsilon |E|$ in $O\left(\frac{\log(1/\varepsilon)}{\varepsilon^4}\right)$ rounds using $O\left(\log(1/\varepsilon)\right)$ shared random bits. Thus, for every constant $\varepsilon>0$, the round complexity is $O(1)$, independent of the number of vertices and the maximum degree. Previous algorithms achieve constant round complexity only for bounded-degree or almost-regular graphs; on general graphs, their round complexity depends polylogarithmically on $n$. Our main technical idea is a degree-guarded freezing rule that allows widely varying degrees to be handled by a single global charging argument, avoiding the $\Theta(\log n)$ successive degree thresholds used in previous work. The shared random bits are used only to select a common random output iteration. As consequences, we obtain an $O\left( \frac{\log(1/\varepsilon)}{\varepsilon^4} + \frac{\log n}{\varepsilon} \right)$-round $\congest$ algorithm without pre-shared randomness, via a low-diameter decomposition, and an $O\left(\frac{\log(1/\varepsilon)}{\varepsilon^4}\right)$-round algorithm in the fully-scalable Massively Parallel Computation ($\mpc$) model with linear total memory.

cs.DC↗

arXiv2026

Local Certification of Vertex and Edge Connectivity

Local certification is a framework for verifying global graph properties using only local information. In this model, a prover assigns short labels, called certificates, to the vertices of a graph. Each vertex then exchanges certificates with its neighbors and performs a purely local check to determine whether the graph satisfies the desired property. This line of research has led to efficient certification schemes for a broad range of graph classes, including minor-closed families, topological graph classes, and graphs defined by forbidden subgraphs. In this paper, we study the local certification of graph connectivity. Prior work by Bousquet, Feuilloley, and Pierron (JPDC 2024) showed that $2$-vertex-connectivity, $2$-edge-connectivity, and $3$-vertex-connectivity admit $O(\log n)$-bit certificates, leveraging structural characterizations such as ear decompositions. We go substantially beyond these cases and investigate general $k$-vertex-connectivity and $k$-edge-connectivity. We develop new approaches that exploit connections between connectivity and combinatorial structures, including branchings, Eulerian subgraphs, and independent spanning trees. For $k$-edge-connectivity, we obtain an $O_k(\log n)$-bit certification scheme and prove a matching $\Omega_k(\log n)$ lower bound for every $k\ge 3$. The lower bound also applies to $k$-vertex-connectivity. For $k$-vertex-connectivity, we obtain $\tilde{O}_k(\sqrt{n})$-bit certificates for every $k$ under a conjecture of Itai and Zehavi. We further show that, for $k=2$, the logarithmic barrier can be broken on sparse graph classes: $2$-edge-connectivity admits constant-size certificates in bounded-expansion graphs, and $2$-vertex-connectivity admits constant-size certificates in bounded-degree graphs. In contrast, for $2$-vertex-connectivity in general graphs, we prove an $\Omega(\log(\log^\ast n))$-bit lower bound.

cs.DC↗

arXiv2026

Energy-Efficient Aggregation and Minimum-Degree Spanning Trees in Radio Networks

We study the aggregation problem in synchronous multi-hop radio networks with $O(\log n)$-bit messages and no collision detection. Each node initially holds a value, and the goal is to compute a global aggregate such as the sum of all values. Aggregation tasks arise naturally in wireless sensor networks, where nodes are often battery-powered and radio activity is the dominant source of energy consumption. Accordingly, our main objective is to minimize the energy complexity, defined as the maximum number of rounds in which any node is awake. Our main result is a randomized distributed algorithm that, with high probability, constructs and executes an aggregation schedule in $O(n \operatorname{polylog} n)$ rounds and using $O(\Delta^\ast \operatorname{polylog} n)$ energy, where $\Delta^\ast$ is the minimum possible maximum degree of a spanning tree of the network graph. This guarantee is nearly optimal: for any aggregation schedule and any graph, there exists a node that must be awake for at least $\Delta^\ast$ rounds. As a by-product, the algorithm also computes a spanning tree whose maximum degree is within an $O(\log n)$ factor of $\Delta^\ast$, with the same round and energy guarantees. For every tree edge, both endpoints learn that the edge belongs to the tree.

cs.DC↗

arXiv2026

Efficient Counting and Simulation in Content-Oblivious Rings

In the content-oblivious (CO) model (proposed by Censor-Hillel et al.), processes inhabit an asynchronous network and communicate only by exchanging pulses. A series of works has clarified the computational power of this model. In particular, it was shown that, when a leader is present and the network is 2-edge-connected, content-oblivious communication can simulate classical asynchronous message passing. Subsequent results extended this equivalence to leaderless oriented and unoriented rings, and, under non-uniform assumptions, to general 2-edge-connected networks. The simulator of Censor-Hillel et al. requires $O(n^3b+n^3\log n)$ pulses to emulate the send of a single $b$-bit message, making it impractical even on modest-size networks. We focus on message-efficient computation in CO networks. We study the fundamental problem of counting in ring topologies, both because knowing the exact network size is a basic prerequisite for many distributed tasks and because counting immediately implies a broad class of aggregation primitives. We give an algorithm that counts using $O(n^{1.5})$ pulses in anonymous rings with a leader, an $O(n\log^2 n)$ algorithm for counting in rings with IDs. Moreover, we show that any counting algorithm in CO requires $Ω(n\log n)$ pulses. Interestingly, in the course of this investigation, we design a simulator for classic message passing: in one simulated round, each process can send a $b$-bit message to each of its neighbors using only $O(b)$ pulses per process. The simulator extends to general 2-edge-connected networks, after a pre-processing step that requires $O(n^{8}\log n)$ pulses, where $n$ is the number of processes, allowing thus efficient simulation of asynchronous message passing in general 2-edge-connected networks.

cs.DC↗

arXiv2026

The Complexity of Distributed Minimum Weight Cycle Approximation

We study the Minimum Weight Cycle (MWC) problem in the $\mathsf{CONGEST}$ model of distributed computing. For undirected weighted graphs, we give a randomized $(k+1)$-approximation algorithm for every \underline{real number} $k \geq (1+\sqrt{5})/2 \approx 1.618$. The algorithm runs in \[ \tilde{O}\left(n^{\frac{k+1}{2k+1}} + D\right) \] rounds, where $n$ is the number of nodes and $D$ is the unweighted diameter of the graph. Varying $k$ therefore yields a smooth trade-off between approximation ratio and round complexity. On the lower-bound side, assuming the Erd\H{o}s girth conjecture, we prove that for every \underline{integer} $k \geq 1$ and every $\epsilon > 0$, any randomized $(k+1-\epsilon)$-approximation algorithm for MWC requires \[ \tilde{\Omega}\left(n^{\frac{k+1}{2k+1}}+D\right) \] rounds. The lower bound holds for both directed unweighted graphs and undirected weighted graphs, even on graphs of diameter $\Theta(\log n)$. Consequently, for every integer $k \geq 2$, our upper and lower bounds for undirected weighted graphs match up to polylogarithmic factors. This gives a nearly tight characterization of the round complexity of approximate MWC across an infinite family of approximation ratios. These results improve the previous state of the art of Manoharan and Ramachandran (PODC 2024), who gave a $(2+\epsilon)$-approximation algorithm for undirected weighted graphs in $\tilde{O}(n^{2/3}+D)$ rounds, and proved an $\tilde{\Omega}(\sqrt{n})$ lower bound for arbitrary approximation ratios in directed unweighted and undirected weighted graphs.

cs.DC↗

arXiv2026

Efficient Distributed Decomposition and Routing Algorithms in Minor-Free Networks and Their Applications

In the LOCAL model, low-diameter decomposition is a useful tool in designing algorithms, as it allows us to shift from the general graph setting to the low-diameter graph setting, where brute-force information gathering can be done efficiently. Recently, Chang and Su [PODC 2022] showed that any high-conductance network excluding a fixed minor contains a high-degree vertex, so the entire graph topology can be gathered to one vertex efficiently in the CONGEST model using expander routing. Therefore, in networks excluding a fixed minor, many problems that can be solved efficiently in LOCAL via low-diameter decomposition can also be solved efficiently in CONGEST via expander decomposition. In this work, we show improved decomposition and routing algorithms for networks excluding a fixed minor in the CONGEST model. Our algorithms cost $\text{poly}(\log n, 1/ε)$ rounds deterministically. For bounded-degree graphs, our algorithms finish in $O(ε^{-1}\log n) + ε^{-O(1)}$ rounds. Our algorithms have a wide range of applications, including the following results in CONGEST. 1. A $(1-ε)$-approximate maximum independent set in a network excluding a fixed minor can be computed deterministically in $O(ε^{-1}\log^\ast n) + ε^{-O(1)}$ rounds, nearly matching the $Ω(ε^{-1}\log^\ast n)$ lower bound of Lenzen and Wattenhofer [DISC 2008]. 2. Property testing of any additive minor-closed property can be done deterministically in $O(\log n)$ rounds if $ε$ is a constant or $O(ε^{-1}\log n) + ε^{-O(1)}$ rounds if the maximum degree $Δ$ is a constant, nearly matching the $Ω(ε^{-1}\log n)$ lower bound of Levi, Medina, and Ron [PODC 2018].

cs.DS↗

arXiv2026

Improved All-Pairs Approximate Shortest Paths in Congested Clique

In this paper, we present a new randomized $O(1)$-approximation algorithm for the All-Pairs Shortest Paths (APSP) problem in weighted undirected graphs that runs in just $O(\log \log \log n)$ rounds in the Congested-Clique model. Before our work, the fastest algorithms achieving an $O(1)$-approximation for APSP in weighted undirected graphs required $\operatorname{poly}(\log n)$ rounds, as shown by Censor-Hillel, Dory, Korhonen, and Leitersdorf (PODC 2019 & Distributed Computing 2021). In the unweighted undirected setting, Dory and Parter (PODC 2020 & Journal of the ACM 2022) obtained $O(1)$-approximation in $\operatorname{poly}(\log \log n)$ rounds. By terminating our algorithm early, for any given parameter $t \geq 1$, we obtain an $O(t)$-round algorithm that guarantees an $O\left(\log^{1/2^t} n\right)$ approximation in weighted undirected graphs. This tradeoff between round complexity and approximation factor offers flexibility, allowing the algorithm to adapt to different requirements. In particular, for any constant $\varepsilon > 0$, an $O\left(\log^\varepsilon n\right)$-approximation can be obtained in $O(1)$ rounds. Previously, $O(1)$-round algorithms were only known for $O(\log n)$-approximation, as shown by Chechik and Zhang (PODC 2022). A key ingredient in our algorithm is a lemma that, under certain conditions, allows us to improve an $a$-approximation for APSP to an $O(\sqrt{a})$-approximation in $O(1)$ rounds. To prove this lemma, we develop several new techniques, including an $O(1)$-round algorithm for computing the $k$-nearest nodes, as well as new types of hopsets and skeleton graphs based on the notion of $k$-nearest nodes.

cs.DS↗

arXiv2025

Deterministic Distributed Algorithms and Measurable Combinatorics on $Δ$-Regular Forests

We investigate the connections between the fields of distributed computing and measurable combinatorics by considering complexity classes of locally checkable labeling problems on regular forests. We show that the most important deterministic complexity classes from the LOCAL model of distributed computing exactly coincide with well-studied classes in measurable combinatorics. Namely, first we show that a locally checkable labeling problem admits a continuous solution if and only if it can be solved by a deterministic local algorithm with complexity $O(\log^* n)$. Second, our main result states that, surprisingly, a locally checkable labeling problem admits a Baire measurable solution if and only if it can be solved by a local algorithm with complexity $O(\log n)$. These theorems suggest the existence of deeper connections between the two frameworks. Furthermore, the latter result relies on a complete combinatorial characterization of the classes in question, and as a by-product, it shows that membership in these classes is decidable.

math.LO↗

arXiv2025

Beyond 2-Edge-Connectivity: Algorithms and Impossibility for Content-Oblivious Leader Election

The content-oblivious model, introduced by Censor-Hillel, Cohen, Gelles, and Sel (PODC 2022; Distributed Computing 2023), captures an extremely weak form of communication where nodes can only send asynchronous, content-less pulses. Censor-Hillel, Cohen, Gelles, and Sel showed that no non-constant function $f(x,y)$ can be computed correctly by two parties using content-oblivious communication over a single edge, where one party holds $x$ and the other holds $y$. This seemingly ruled out many natural graph problems on non-2-edge-connected graphs. In this work, we show that, with the knowledge of network topology $G$, leader election is possible in a wide range of graphs. Impossibility: Graphs symmetric about an edge admit no randomized terminating leader election algorithm, even when nodes have unique identifiers and full knowledge of $G$. Leader election algorithms: Trees that are not symmetric about any edge admit a quiescently terminating leader election algorithm with topology knowledge, even in anonymous networks, using $O(n^2)$ messages, where $n$ is the number of nodes. Moreover, even-diameter trees admit a terminating leader election given only the knowledge of the network diameter $D = 2r$, with message complexity $O(nr)$. Necessity of topology knowledge: In the family of graphs $\mathcal{G} = \{P_3, P_5\}$, both the 3-path $P_3$ and the 5-path $P_5$ admit a quiescently terminating leader election if nodes know the topology exactly. However, if nodes only know that the underlying topology belongs to $\mathcal{G}$, then terminating leader election is impossible.

cs.DC↗

arXiv2025

Narrowing the LOCAL$\unicode{x2013}$CONGEST Gaps in Sparse Networks via Expander Decompositions

Many combinatorial optimization problems can be approximated within $(1 \pm ε)$ factors in $\text{poly}(\log n, 1/ε)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches require sending messages of unlimited size, so they do not extend to the CONGEST model, which restricts the message size to be $O(\log n)$ bits. In this paper, we develop a generic framework for obtaining $\text{poly}(\log n, 1/ε)$-round $(1\pm ε)$-approximation algorithms for many combinatorial optimization problems, including maximum weighted matching, maximum independent set, and correlation clustering, in graphs excluding a fixed minor in the CONGEST model. This class of graphs covers many sparse network classes that have been studied in the literature, including planar graphs, bounded-genus graphs, and bounded-treewidth graphs. Furthermore, we show that our framework can be applied to give an efficient distributed property testing algorithm for an arbitrary minor-closed graph property that is closed under taking disjoint union, significantly generalizing the previous distributed property testing algorithm for planarity in [Levi, Medina, and Ron, PODC 2018 & Distributed Computing 2021]. Our framework uses distributed expander decomposition algorithms [Chang and Saranurak, FOCS 2020] to decompose the graph into clusters of high conductance. We show that any graph excluding a fixed minor admits small edge separators. Using this result, we show the existence of a high-degree vertex in each cluster in an expander decomposition, which allows the entire graph topology of the cluster to be routed to a vertex. Similar to the use of network decompositions in the LOCAL model, the vertex will be able to perform any local computation on the subgraph induced by the cluster and broadcast the result over the cluster.

cs.DS↗

arXiv2025

Overlay Network Construction: Improved Overall and Node-Wise Message Complexity

We consider the problem of constructing distributed overlay networks, where nodes in a reconfigurable system can create or sever connections with nodes whose identifiers they know. Initially, each node knows only its own and its neighbors' identifiers, forming a local channel, while the evolving structure is termed the global channel. The goal is to reconfigure any connected graph into a desired topology, such as a bounded-degree expander graph or a well-formed tree (WFT) with a constant maximum degree and logarithmic diameter, minimizing the total number of rounds and message complexity. This problem mirrors real-world peer-to-peer network construction, where creating robust and efficient systems is desired. We study the overlay reconstruction problem in a network of $n$ nodes in two models: \textsf{GOSSIP-reply}{} and \textsf{HYBRID}{}. In the \textsf{GOSSIP-reply}{} model, each node can send a message and receive a corresponding reply message in one round. In the \textsf{HYBRID}{} model, a node can send $O(1)$ messages to each neighbor in the local channel and a total of $O(\log n)$ messages in the global channel. In both models, we propose protocols for WFT construction with $O\left(n \log n\right)$ message complexities using messages of $O(\log n)$ bits. In the \textsf{GOSSIP-reply}{} model, our protocol takes $O(\log n)$ rounds while in the \textsf{HYBRID} model, our protocol takes $O(\log^2 n)$ rounds. Both protocols use $O\left(n \log^2 n\right)$ bits of communication.

cs.DC↗

arXiv2025

Non-Uniform Content-Oblivious Leader Election on Oriented Asynchronous Rings

We study the leader election problem in oriented ring networks under content-oblivious asynchronous message-passing systems, where an adversary may arbitrarily corrupt message contents. Frei et al. (DISC 2024) presented a uniform terminating leader election algorithm for oriented rings in this setting, with message complexity $O(n \cdot \mathsf{ID}_{\max})$ on a ring of size $n$, where $\mathsf{ID}_{\max}$ is the largest identifier in the system, this result has been recently extended by Chalopin et al. (DISC 2025) to unoriented rings. In this paper, we investigate the message complexity of leader election on ring networks in the content-oblivious model, showing that no uniform algorithm can solve the problem if each process is limited to sending a constant number of messages in one direction. Interestingly, this limitation hinges on the uniformity assumption. In the non-uniform setting, where processes know an upper bound $U \geq n$ on the ring size, we present an algorithm with message complexity $O(n \cdot U \cdot \mathsf{ID}_{\min})$, in which each process sends $O(U \cdot \mathsf{ID}_{\min})$ messages clockwise and only three messages counter-clockwise. Here, $\mathsf{ID}_{\min}$ is the smallest identifier in the system. This dependence on the identifiers compares favorably with the dependence on $\mathsf{ID}_{\max}$ of Frei et al. We also show a non-uniform algorithm where each process sends $O(U \cdot \log\mathsf{ID}_{\min})$ messages in one direction and $O(\log\mathsf{ID}_{\min})$ in the other. The factor $\log \mathsf{ID}_{\min}$ is optimal, matching the lower bound of Frei et al. Finally, in the anonymous setting, where processes do not have identifiers, we propose a randomized algorithm where each process sends only $O(\log^2 U)$ messages, with a success probability of $1 - U^{-c}$.

cs.DC↗

arXiv2025

Optimal Distributed Replacement Paths

We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$. For unweighted directed graphs, we establish the tight randomized round complexity bound for this problem as $\widetildeΘ(n^{2/3} + D)$ by showing matching upper and lower bounds. Our upper bound extends to $(1+ε)$-approximation for weighted directed graphs. Our lower bound applies even to the second simple shortest path problem, which asks only for the smallest replacement path length. These results improve upon the very recent work of Manoharan and Ramachandran (SIROCCO 2024), who showed a lower bound of $\widetildeΩ(n^{1/2} + D)$ and an upper bound of $\widetilde{O}(n^{2/3} + \sqrt{n h_{st}} + D)$, where $h_{st}$ is the number of hops in the given $s$-$t$ shortest path $P$.

cs.DS↗

arXiv2025

Femtojoule-per-operation photonic computer for the subset sum problem

Energy-efficient computing is becoming increasingly important in the information era. However, electronic computers with von Neumann architecture can hardly meet the challenge due to the inevitable energy-intensive data movement, especially when tackling computationally hard problems or complicated tasks. Here, we experimentally demonstrate an energy-efficient photonic computer that solves intractable subset sum problem (SSP) by making use of the extremely low energy level of photons (~10^(-19) J) and a time-of-flight storage technique. We show that the energy consumption of the photonic computer maintains no larger than 10^(-15) J per operation at a reasonably large problem size N=33, and it consumes 10^(8) times less energy than the most energy-efficient supercomputer for a medium-scale problem. In addition, when the photonic computer is applied to deal with real-life problems that involves iterative computation of the SSP, the photonic advantage in energy consumption is further enhanced and massive energy can be saved. Our results indicate the superior competitiveness of the photonic computer in the energy costs of complex computation, opening a possible path to green computing.

physics.optics↗

arXiv2025

The Complexity Landscape of Dynamic Distributed Subgraph Finding

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 \emph{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.

cs.DS↗

arXiv2025

Content-Oblivious Leader Election in 2-Edge-Connected Networks

Censor-Hillel, Cohen, Gelles, and Sela (PODC 2022 & Distributed Computing 2023) studied fully-defective asynchronous networks, where communication channels may suffer an extreme form of alteration errors, rendering messages completely corrupted. The model is equivalent to content-oblivious computation, where nodes communicate solely via pulses. They showed that if the network is 2-edge-connected, then any algorithm for a noiseless setting can be simulated in the fully-defective setting; otherwise, no non-trivial computation is possible in the fully-defective setting. However, their simulation requires a predesignated leader, which they conjectured to be necessary for any non-trivial content-oblivious task. In this work, we present two results: General 2-edge-connected topologies: First, we show an asynchronous content-oblivious leader election algorithm that quiescently terminates in any 2-edge-connected network with message complexity $O(m \cdot N \cdot \mathsf{ID}_{\min})$, where $m$ is the number of edges, $N$ is a known upper bound on the number of nodes, and $\mathsf{ID}_{\min}$ is the smallest $\mathsf{ID}$. Combined with the above simulation, this result shows that whenever a size bound $N$ is known, any noiseless algorithm can be simulated in the fully-defective model without a preselected leader, fully refuting the conjecture. Unoriented rings: We then show that the knowledge of $N$ can be dropped in unoriented ring topologies by presenting a quiescently terminating election algorithm with message complexity $O(n \cdot \mathsf{ID}_{\max})$ that matches the previous bound. Consequently, this result constitutes a strict improvement over the previous leader election in oriented rings by Frei, Gelles, Ghazy, and Nolin (DISC 2024) and shows that, on rings, fully-defective and noiseless communication are computationally equivalent, with no additional assumptions.

cs.DC↗

arXiv2025

Bounded Memory in Distributed Networks

The recent advent of programmable switches makes distributed algorithms readily deployable in real-world datacenter networks. However, there are still gaps between theory and practice that prevent the smooth adaptation of CONGEST algorithms to these environments. In this paper, we focus on the memory restrictions that arise in real-world deployments. We introduce the $μ$-CONGEST model where on top of the bandwidth restriction, the memory of nodes is also limited to $μ$ words, in line with real-world systems. We provide fast algorithms of two main flavors. First, we observe that many algorithms in the CONGEST model are memory-intensive and do not work in $μ$-CONGEST. A prime example of a family of algorithms that use large memory is clique-listing algorithms. We show that the memory issue that arises here cannot be resolved without incurring a cost in the round complexity, by establishing a lower bound on the round complexity of listing cliques in $μ$-CONGEST. We introduce novel techniques to overcome these issues and generalize the algorithms to work within a given memory bound. Combined with our lower bound, these provide tight tradeoffs between the running time and memory of nodes. Second, we show that it is possible to efficiently simulate various families of streaming algorithms in $μ$-CONGEST. These include fast simulations of $p$-pass algorithms, random order streams, and various types of mergeable streaming algorithms. Combining our contributions, we show that we can use streaming algorithms to efficiently generate statistics regarding combinatorial structures in the network. An example of an end result of this type is that we can efficiently identify and provide the per-color frequencies of the frequent monochromatic triangles in $μ$-CONGEST.

cs.DC↗