相关论文: Parallel Derandomization for Coloring

Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…

We consider two models of computation: centralized local algorithms and local distributed algorithms. Algorithms in one model are adapted to the other model to obtain improved algorithms. Distributed vertex coloring is employed to design…

Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…

We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…

A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…

We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit…

Graph Coloring Problem (GCP) is an NP-Hard vertex labeling problem in graphs such that no two adjacent vertices can have the same color. Large instances of GCP cannot be solved in reasonable execution times by exact algorithms. Therefore,…

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with Luby (1993) and continuing with Berger…

This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…

We study the deterministic complexity of the $2$-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. Linear MPC: We present a constant-round deterministic algorithm for…

Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…

Given a dynamic graph $G$ with $n$ vertices and $m$ edges subject to insertion an deletions of edges, we show how to maintain a $(1+\varepsilon)\Delta$-edge-colouring of $G$ without the use of randomisation. More specifically, we show a…

Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…

This paper addresses the cornerstone family of \emph{local problems} in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in…

The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number…

Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for…

This paper is concerned with efficiently coloring sparse graphs in the distributed setting with as few colors as possible. According to the celebrated Four Color Theorem, planar graphs can be colored with at most 4 colors, and the proof…