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Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover,…
We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…
In this note we show that local equilibrium equations (the generalization of the TAP equations or of the belief propagation equations) do have solutions in the colorable phase of the coloring problem. The same results extend to other…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the…
The Lov\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its…
NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…
There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…
The importance of classifying connections in large graphs has been the motivation for a rich line of work on distributed subgraph finding that has led to exciting recent breakthroughs. A crucial aspect that remained open was whether…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…
Designing models that are both expressive and preserve known invariances of tasks is an increasingly hard problem. Existing solutions tradeoff invariance for computational or memory resources. In this work, we show how to leverage…
The gap between the known randomized and deterministic local distributed algorithms underlies arguably the most fundamental and central open question in distributed graph algorithms. In this paper, we develop a generic and clean recipe for…
Given a graph with positive and negative edge labels, the correlation clustering problem aims to cluster the nodes so to minimize the total number of between-cluster positive and within-cluster negative edges. This problem has many…
It is shown that for any fixed $c \geq 3$ and $r$, the maximum possible chromatic number of a graph on $n$ vertices in which every subgraph of radius at most $r$ is $c$ colorable is $\tilde{\Theta}\left(n ^ {\frac{1}{r+1}} \right)$ (that…
We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings…
We present ${\rm poly\log\log n}$-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into $k$ parts such that a node of degree $d(u)$ has $\approx d(u)/k$ neighbors in each part. Our…
Tensors are a fundamental operation in distributed computing, \emph{e.g.,} machine learning, that are commonly distributed into multiple parallel tasks for large datasets. Stragglers and other failures can severely impact the overall…
Large language models (LLMs) exhibit remarkable flexibility: they can adapt to novel tasks from in-context examples without any parameter updates, a capability known as in-context learning (ICL). Prior work on synthetic tasks has shown that…