Related papers: Balanced Allocation on Graphs
We study the placement of n balls into n bins where balls and bins are represented as two vector spaces over Z 2 . The placement is done according to a linear transformation between the two vector spaces. We analyze the expected size of a…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
We study the repeated balls-into-bins process introduced by Becchetti, Clementi, Natale, Pasquale and Posta (2019). This process starts with $m$ balls arbitrarily distributed across $n$ bins. At each round $t=1,2,\ldots$, one ball is…
A graph $d$-process starts with an empty graph on $n$ vertices, and adds one edge at each time step, chosen uniformly at random from those pairs which are not yet edges and whose both vertices have current degree less than $d$. If, in the…
In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…
We consider the question of how many edge-disjoint near-maximal cliques may be found in the dense Erd\H{o}s-R\'enyi random graph $G(n,p)$. Recently Acan and Kahn showed that the largest such family contains only $O(n^2/(\log{n})^3)$…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…
Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only…
This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…
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…
We propose a simple distributed algorithm for balancing indivisible tokens on graphs. The algorithm is completely deterministic, though it tries to imitate (and enhance) a random algorithm by keeping the accumulated rounding errors as small…
We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and…
Finding the node with the largest label in a network, modeled as an undirected connected graph, is one of the fundamental problems in distributed computing. This is the way in which $\textit{leader election}$ is usually solved. We consider…
Load balancing is a well-studied problem, with balls-in-bins being the primary framework. The greedy algorithm $\mathsf{Greedy}[d]$ of Azar et al. places each ball by probing $d > 1$ random bins and placing the ball in the least loaded of…
We consider the following balls-into-bins process with $n$ bins and $m$ balls: each ball is equipped with a mutually independent exponential clock of rate 1. Whenever a ball's clock rings, the ball samples a random bin and moves there if…
OBDD-based graph algorithms deal with the characteristic function of the edge set E of a graph $G = (V,E)$ which is represented by an OBDD and solve optimization problems by mainly using functional operations. We present an OBDD-based…
In this paper we study dynamic averaging load balancing on general graphs. We consider infinite time and dynamic processes, where in every step new load items are assigned to randomly chosen nodes. A matching is chosen, and the load is…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…
Let $H_n$ be a graph on $n$ vertices and let $\ber{H_n}$ denote the complement of $H_n$. Suppose that $\Delta = \Delta(n)$ is the maximum degree of $\ber{H_n}$. We analyse three algorithms for sampling $d$-regular subgraphs ($d$-factors) of…