Related papers: Low-Memory Algorithms for Online and W-Streaming E…
In this paper we show that every graph $G$ of bounded maximum average degree ${\rm mad}(G)$ and with maximum degree $\Delta$ can be edge-colored using the optimal number of $\Delta$ colors in quasilinear time, whenever $\Delta\ge 2{\rm…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
We study the problem of online coloring for graphs with large odd girth. The best previously known algorithm uses $O(n^{1/2})$ colors, which was discovered by Kierstead in 1998. This algorithm works when the odd girth is 7 or more. In this…
In the $\ell$-Coloring Problem, we are given a graph on $n$ nodes, and tasked with determining if its vertices can be properly colored using $\ell$ colors. In this paper we study below-guarantee graph coloring, which tests whether an…
We introduce the poly-streaming model, a generalization of streaming models of computation in which $k$ processors process $k$ data streams containing a total of $N$ items. The algorithm is allowed $O\left(f(k)\cdot M_1\right)$ space, where…
Let $\epsilon \in (0, 1)$ and $n, \Delta \in \mathbb N$ be such that $\Delta = \Omega\left(\max\left\{\frac{\log n}{\epsilon},\, \left(\frac{1}{\epsilon}\log \frac{1}{\epsilon}\right)^2\right\}\right)$. Given an $n$-vertex $m$-edge simple…
Depth first search is a fundamental graph problem having a wide range of applications. For a graph $G=(V,E)$ having $n$ vertices and $m$ edges, the DFS tree can be computed in $O(m+n)$ using $O(m)$ space where $m=O(n^2)$. In the streaming…
We explore the use of local algorithms in the design of streaming algorithms for the Maximum Directed Cut problem. Specifically, building on the local algorithm of Buchbinder et al. (FOCS'12) and Censor-Hillel et al. (ALGOSENSORS'17), we…
We consider the problem of linearly ordered (LO) coloring of hypergraphs. A hypergraph has an LO coloring if there is a vertex coloring, using a set of ordered colors, so that (i) no edge is monochromatic, and (ii) each edge has a unique…
The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed…
We study the performance of sequential contention resolution and matching algorithms on random graphs with vanishing edge probabilities. When the edges of the graph are processed in an adversarially-chosen order, we derive a new OCRS that…
In this paper we evaluate distributed node coloring algorithms for wireless networks using the network simulator Sinalgo [by DCG@ETHZ]. All considered algorithms operate in the realistic signal-to-interference-and-noise-ratio (SINR) model…
We study the communication complexity of $(\Delta + 1)$ vertex coloring, where the edges of an $n$-vertex graph of maximum degree $\Delta$ are partitioned between two players. We provide a randomized protocol which uses $O(n)$ bits of…
Many complex systems and datasets are characterized by multiway interactions of different categories, and can be modeled as edge-colored hypergraphs. We focus on clustering such datasets using the NP-hard edge-colored clustering problem,…
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…
We study a version of online edge coloring, where the goal is to color as many edges as possible using only a given number, $k$, of available colors. All of our results are with regard to competitive analysis. Previous attempts to identify…
We provide the first online algorithm for spectral hypergraph sparsification. In the online setting, hyperedges with positive weights are arriving in a stream, and upon the arrival of each hyperedge, we must irrevocably decide whether or…
Coloring line art images based on the colors of reference images is an important stage in animation production, which is time-consuming and tedious. In this paper, we propose a deep architecture to automatically color line art videos with…
The vertex coloring problem has received a lot of attention in the context of synchronous round-based systems where, at each round, a process can send a message to all its neighbors, and receive a message from each of them. Hence, this…