Related papers: Fault Tolerant Coloring of the Asynchronous Cycle
A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of…
We give a new, simple distributed algorithm for graph colouring in paths and cycles. Our algorithm is fast and self-contained, it does not need any globally consistent orientation, and it reduces the number of colours from $10^{100}$ to $3$…
The distributed coloring problem is arguably one of the key problems studied in the area of distributed graph algorithms. The most standard variant of the problem asks for a proper vertex coloring of a graph with $\Delta+1$ colors, where…
Register allocation, which is a crucial phase of a good optimizing compiler, relies on graph coloring. Hence, an efficient graph coloring algorithm is of paramount importance. In this work we try to learn a good heuristic for coloring…
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is…
We give a linear-time algorithm to decide 3-colorability of a triangle-free graph embedded in a fixed surface, and a quadratic-time algorithm to output a 3-coloring in the affirmative case. The algorithms also allow to prescribe the…
We consider the clock synchronization problem in the (discrete) beeping model: Given a network of $n$ nodes with each node having a clock value $\delta(v) \in \{0,\ldots T-1\}$, the goal is to synchronize the clock values of all nodes such…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the…
We study the edge-coloring problem in simple $n$-vertex $m$-edge graphs with maximum degree $\Delta$. This is one of the most classical and fundamental graph-algorithmic problems. Vizing's celebrated theorem provides…
We develop an efficient parallel distributed algorithm for matrix completion, named NOMAD (Non-locking, stOchastic Multi-machine algorithm for Asynchronous and Decentralized matrix completion). NOMAD is a decentralized algorithm with…
We study the self-stabilizing leader election problem in anonymous $n$-nodes networks. Achieving self-stabilization with low space memory complexity is particularly challenging, and designing space-optimal leader election algorithms remains…
We consider the problem of optimal unsignalized intersection management, wherein we seek to obtain safe and optimal trajectories, for a set of robots that arrive randomly and continually. This problem involves repeatedly solving a mixed…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a…
Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a…
For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the former needs edges to be assigned colors immediately after insertion, typically without any space restrictions, while the latter limits memory to…
For any $\Delta$, let $k_\Delta$ be the maximum integer $k$ such that $(k+1)(k+2)\le \Delta$. We give a distributed \LOCAL algorithm that, given an integer $k < k_\Delta$, computes a valid $\Delta-k$-coloring if one exists. The algorithm…
For every even positive integer $k\ge 4$ let $f(n,k)$ denote the minimim number of colors required to color the edges of the $n$-dimensional cube $Q_n$, so that the edges of every copy of $k$-cycle $C_k$ receive $k$ distinct colors.…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…