Related papers: Simple dynamic algorithms for Maximal Independent …
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
Maximal Independent Set (MIS) in a graph is a fundamental problem with applications in resource allocation, scheduling, and network optimization. Although graphs are inherently un-structured and challenging for GPU parallelism due to…
With few exceptions (namely, algorithms for maximal matching, $2$-approximate vertex cover, and certain constant-stretch spanners), all known fully dynamic algorithms in general graphs require (amortized) $\Omega(\log n)$ update/query time.…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
We study the maximum matching problem in fully dynamic graphs: a graph is undergoing both edge insertions and deletions, and the goal is to efficiently maintain a large matching after each edge update. This problem has received considerable…
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic…
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore…
In this study, we address the independent set enumeration problem. Although several efficient enumeration algorithms and careful analyses have been proposed for maximal independent sets, no fine-grained analysis has been given for the…
Motivated by the increasing need to understand the algorithmic foundations of distributed large-scale graph computations, we study a number of fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matching ${\cal M}$ whose weight is at least $1/8 M^{*}$ where $M^{*}$ is the weight of the…
During the last 10 years it has become popular to study dynamic graph problems in a emergency planning or sensitivity setting: Instead of considering the general fully dynamic problem, we only have to process a single batch update of size…
We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as…
In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…
We consider the problem of maintaining an approximately maximum (fractional) matching and an approximately minimum vertex cover in a dynamic graph. Starting with the seminal paper by Onak and Rubinfeld [STOC 2010], this problem has received…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. It has been suggested that finding an MIS is equivalent to computing a maximum matching of the network, where…
Chatterjee, Gmyr, and Pandurangan [PODC 2020] recently introduced the notion of awake complexity for distributed algorithms, which measures the number of rounds in which a node is awake. In the other rounds, the node is sleeping and…
Motivated by recent applications of dominator computations, we consider the problem of dynamically maintaining the dominators of flow graphs through a sequence of insertions and deletions of edges. Our main theoretical contribution is a…
The complexity of classical computational problems in graph classes defined by forbidding induced subgraphs is one of the central topics of algorithmic graph theory. Recently, there has been a growing interest in the complexity of such…
Mobile agents have emerged as a powerful framework for solving fundamental graph problems in distributed settings in recent times. These agents, modelled as autonomous physical or software entities, possess local computation power, finite…