Related papers: Bounded Independence Edge Sampling for Combinatori…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…
Analyzing massive data sets has been one of the key motivations for studying streaming algorithms. In recent years, there has been significant progress in analysing distributions in a streaming setting, but the progress on graph problems…
The celebrated theorem of Chung, Graham, and Wilson on quasirandom graphs implies that if the 4-cycle and edge counts in a graph $G$ are both close to their typical number in $\mathbb{G}(n,1/2),$ then this also holds for the counts of…
This paper presents significantly improved deterministic algorithms for some of the key problems in the area of distributed graph algorithms, including network decomposition, hitting sets, and spanners. As the main ingredient in these…
We study the algorithmic task of finding a large independent set in a sparse Erd\H{o}s-R\'{e}nyi random graph with $n$ vertices and average degree $d$. The maximum independent set is known to have size $(2 \log d / d)n$ in the double limit…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
In a recent breakthrough work, Gartland and Lokshtanov [FOCS 2020] showed a quasi-polynomial-time algorithm for Maximum Weight Independent Set in $P_t$-free graphs, that is, graphs excluding a fixed path as an induced subgraph. Their…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under…
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…
Maintaining a $k$-core decomposition quickly in a dynamic graph has important applications in network analysis. The main challenge for designing efficient exact algorithms is that a single update to the graph can cause significant global…
The random intersection graph model $\mathcal G(n,m,p)$ is considered. Due to substantial edge dependencies, studying even fundamental statistics such as the subgraph count is significantly more challenging than in the classical binomial…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
We contribute an approach to the problem of locally computing sparse connected subgraphs of dense graphs. In this setting, given an edge in a connected graph $G = (V, E)$, an algorithm locally decides its membership in a sparse connected…
We study the k-wise independent relaxation of the usual model G(N,p) of random graphs where, as in this model, N labeled vertices are fixed and each edge is drawn with probability p, however, it is only required that the distribution of any…
Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…
Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to…
This study addresses the issue of balancing graph summarization and graph change detection. Graph summarization compresses large-scale graphs into a smaller scale. However, the question remains: To what extent should the original graph be…