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MST in Log-Star Rounds of Congested Clique Open
We present a randomized algorithm that computes a Minimum Spanning Tree (MST) in O(log* n) rounds, with high probability, in the Congested Clique model of distributed computing. In this model, the input is a graph on n nodes, initially eac…
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Faster Polynomial Multiplication over Finite Fields Open
Polynomials over finite fields play a central role in algorithms for cryptography, error correcting codes, and computer algebra. The complexity of multiplying such polynomials is still a major open problem. Let p be a prime, and let M p ( …
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Sublogarithmic Distributed Algorithms for Lov\\'asz Local lemma, and the\n Complexity Hierarchy Open
Locally Checkable Labeling (LCL) problems include essentially all the classic\nproblems of $\\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening\nrevelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded\…
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Weighted min-cut: sequential, cut-query, and streaming algorithms Open
Consider the following 2-respecting min-cut problem. Given a weighted graph\n$G$ and its spanning tree $T$, find the minimum cut among the cuts that contain\nat most two edges in $T$. This problem is an important subroutine in Karger's\nce…
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Improving Performances of Log Mining for Anomaly Prediction Through NLP-Based Log Parsing Open
International audience
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Parallel Graph Connectivity in Log Diameter Rounds Open
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were k…
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Range Predecessor and Lempel-Ziv Parsing Open
The Lempel-Ziv parsing of a string (LZ77 for short) is one of the most important and widely-used algorithmic tools in data compression and string processing. We show that the Lempel-Ziv parsing of a string of length n on an alphabet of siz…
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Fully dynamic connectivity in O(log n(log log n)2) amortized expected time Open
Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a new randomized dynamic connectivity structure with O(log n(log log n)2) amortized expected update time and O(log n/log log log n) query …
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Distributed (Δ +1)-Coloring in Sublogarithmic Rounds Open
We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O (√ log Δ)+ 2 O (√log log n ) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maxima…
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Sleeping is Efficient: MIS in <i>O</i> (1)-rounds Node-averaged Awake Complexity Open
Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the worst-case time for all nodes to finish. The best-known (randomized)…
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A population protocol for exact majority with $O(\\log^{5/3} n)$ stabilization time and asymptotically optimal number of states. Open
A population protocol is a sequence of pairwise interactions of n agents. During one interaction, two randomly selected agents update their states by applying a deterministic transition function. The goal is to stabilize the system at a de…
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Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set Open
This paper presents improved deterministic distributed algorithms, with O(log n)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set…
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<i>O</i> (log <sup>2</sup> <i>k</i> / log log <i>k</i> )-approximation algorithm for directed Steiner tree Open
In the Directed Steiner Tree (DST) problem we are given an n-vertex directed edge-weighted graph, a root r , and a collection of k terminal nodes. Our goal is to find a minimum-cost subgraph that contains a directed path from r to every te…
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Improved Deterministic Distributed Matching via Rounding Open
We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results i…
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Distributed Maximal Independent Set using Small Messages Open
Maximal Independent Set (MIS) is one of the central problems in distributed graph algorithms. The celebrated works of Luby [STOC'85] and Alon, Babai, and Itai [JALG'86] provide O(log n)-round randomized distributed MIS algorithms, which wo…
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A Space-Optimal Grammar Compression Open
A grammar compression is a context-free grammar (CFG) deriving a single string deterministically. For an input string of length N over an alphabet of size sigma, the smallest CFG is O(log N)-approximable in the offline setting and O(log N …
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Distributed Edge Coloring and a Special Case of the Constructive Lovász Local Lemma Open
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree Δ. In this article, we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. Our re…
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Sublogarithmic Distributed Algorithms for Lovász Local Lemma, and the Complexity Hierarchy Open
Locally Checkable Labeling (LCL) problems include essentially all the classic problems of LOCAL distributed algorithms. In a recent enlightening revelation, Chang and Pettie [FOCS'17] showed that any LCL (on bounded degree graphs) that has…
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A Simple <i>O</i>(log log(rank))-Competitive Algorithm for the Matroid Secretary Problem Open
Only recently, progress has been made in obtaining o(log(rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O((log(rank)) 1/2 )-competitive procedure, and Lachish (20…
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Tighter Connections Between Formula-SAT and Shaving Logs Open
A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the {O}(n^2) dynamic programming solution to the Longest Com…
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Communication-efficient randomized consensus Open
We consider the problem of consensus in the challenging classic model. In this model, the adversary is adaptive; it can choose which processors crash at any point during the course of the algorithm. Further, communication is via asynchrono…
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Fully Dynamic Connectivity in <i>O</i>(log <i>n</i>(log log <i>n</i>)<sup>2</sup>) Amortized Expected Time Open
Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a new randomized dynamic connectivity structure with O(log n (log log n)2) amortized expected update time and O(log n/ log log log n) quer…
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Minimum Cut in $O(m\log^2 n)$ Time Open
We give a randomized algorithm that finds a minimum cut in an undirected weighted m-edge n-vertex graph G with high probability in O(m log² n) time. This is the first improvement to Karger’s celebrated O(m log³ n) time algorithm from 1996.…
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Deterministic Subgraph Detection in Broadcast CONGEST Open
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: - For any constant k, detecting k-paths and trees on k nodes can be done in O(1) rounds. - For any c…
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A Comparative study of log volume estimation by using statistical method Open
Log volume estimation is a measurement of the amount of merchantable volume and precise estimation of log volume plays an important role in sustainable forest management. There are several log volume formula which commonly used in estimati…
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An Improved Randomized Data Structure for Dynamic Graph Connectivity Open
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edg…
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Beyond matroids: Secretary Problem and Prophet Inequality with general constraints Open
We study generalizations of the "Prophet Inequality" and "Secretary Problem", where the algorithm is restricted to an arbitrary downward-closed set system. For {0,1}-values, we give O(log n)-competitive algorithms for both problems. This i…
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A Simple Algorithm for Approximating the Text-To-Pattern Hamming Distance Open
The algorithmic task of computing the Hamming distance between a given pattern of length m and each location in a text of length n, both over a general alphabet \Sigma, is one of the most fundamental algorithmic tasks in string algorithms.…
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Beeping a Deterministic Time-Optimal Leader Election Open
The beeping model is an extremely restrictive broadcast communication model that relies only on carrier sensing. In this model, we solve the leader election problem with an asymptotically optimal round complexity of O(D + log n), for a net…
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Local Conflict Coloring Revisited: Linial for Lists. Open
Linial’s famous color reduction algorithm reduces a given m-coloring of a graph with maximum degree Δ to a O(Δ²log m)-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color …