Related papers: Online coloring of short interval graphs and two-c…
Graph colouring is a fundamental problem for networks, serving as a tool for avoiding conflicts via symmetry breaking, for example, avoiding multiple computer processes simultaneously updating the same resource. This paper considers a…
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…
Using the framework of advice complexity, we study the amount of knowledge about the future that an online algorithm needs to color the edges of a graph optimally, i.e., using as few colors as possible. For graphs of maximum degree…
In a 1989 paper titled "shortest paths without a map", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed…
An \emph{interval $t$-coloring} of a multigraph $G$ is a proper edge coloring with colors $1,\dots,t$ such that the colors on the edges incident to every vertex of $G$ are colored by consecutive colors. A \emph{cyclic interval $t$-coloring}…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
We propose a novel way of generalizing the class of interval graphs, via a graph width parameter called the simultaneous interval number. This parameter is related to the simultaneous representation problem for interval graphs and defined…
Motivated by applications where a system must remain operational via continual procurement of contracts, we study two online contract selection problems under uncertain prices. At each time step, a price drawn from a known distribution is…
For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma is colorable from an assignment of lists of size three in time O(|V(G)|). Furthermore, we can allow a subgraph…
In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have…
We consider the edge-weighted online stochastic matching problem, in which an edge-weighted bipartite graph G=(I\cup J, E) with offline vertices J and online vertex types I is given. The online vertices have types sampled from I with…
We consider the problem of online allocation (matching, budgeted allocations, and assortments) of reusable resources where an adversarial sequence of resource requests is revealed over time and any allocated resource is used/rented for a…
Consider the following one-player game played on an initially empty graph with $n$ vertices. At each stage a randomly selected new edge is added and the player must immediately color the edge with one of $r$ available colors. Her objective…
We consider the problem of online interval scheduling on a single machine, where intervals arrive online in an order chosen by an adversary, and the algorithm must output a set of non-conflicting intervals. Traditionally in scheduling…
K\"onig's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every \epsilon > 0 there exists a constant-time distributed algorithm that…
Vizing's theorem asserts the existence of a $(\Delta+1)$-edge coloring for any graph $G$, where $\Delta = \Delta(G)$ denotes the maximum degree of $G$. Several polynomial time $(\Delta+1)$-edge coloring algorithms are known, and the…
The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of GRUNDY COLORING, the problem of determining whether a…
It is known that the online firefighting is 2-competitive on trees (Coupechoux et al. 2019), which suggests that the problem is relatively easy on trees. We extend the study to graphs containing cycles. We first show that the presence of…
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…
Motivated by the use of high speed circuit switches in large scale data centers, we consider the problem of circuit switch scheduling. In this problem we are given demands between pairs of servers and the goal is to schedule at every time…