Related papers: Constructing Low-Redundancy Codes via Distributed …
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
We revisit asynchronous computing in networks of crash-prone processes, under the asynchronous variant of the standard LOCAL model, recently introduced by Fraigniaud et al. [DISC 2022]. We focus on the vertex coloring problem, and our…
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…
We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel…
We consider the problem of constructing deletion correcting codes over a binary alphabet and take a graph theoretic view. An $n$-bit $s$-deletion correcting code is an independent set in a particular graph. We propose constructing such a…
In this paper, we give list coloring variants of simple iterative defective coloring algorithms. Formally, in a list defective coloring instance, each node $v$ of a graph is given a list $L_v$ of colors and a list of allowed defects…
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so…
Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
This paper is centered on the complexity of graph problems in the well-studied LOCAL model of distributed computing, introduced by Linial [FOCS '87]. It is widely known that for many of the classic distributed graph problems (including…
We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…
Linial's famous color reduction algorithm reduces a given $m$-coloring of a graph with maximum degree $\Delta$ to a $O(\Delta^2\log m)$-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to…
In this paper, we consider distributed coloring for planar graphs with a small number of colors. We present an optimal (up to a constant factor) $O(\log{n})$ time algorithm for 6-coloring planar graphs. Our algorithm is based on a novel…
We show an $\Omega\big(\Delta^{\frac{1}{3}-\frac{\eta}{3}}\big)$ lower bound on the runtime of any deterministic distributed $\mathcal{O}\big(\Delta^{1+\eta}\big)$-graph coloring algorithm in a weak variant of the \LOCAL\ model. In…
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…
The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…