Related papers: Distributed Deterministic Exact Minimum Weight Cyc…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on…
The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…
We revisit classical connectivity problems in the CONGEST model of distributed computing. By using techniques from fault tolerant network design, we show improved constructions, some of which are even "local" (i.e., with $\widetilde{O}(1)$…
Round complexity is an extensively studied metric of distributed algorithms. In contrast, our knowledge of the \emph{message complexity} of distributed computing problems and its relationship (if any) with round complexity is still quite…
We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\log^8(n)\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The…
Fine-grained reductions have established equivalences between many core problems with $\tilde{O}(n^3)$-time algorithms on $n$-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second…
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…
Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…
We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree,…
Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…
Given a directed, weighted graph $G=(V,E)$ undergoing edge insertions, the incremental single-source shortest paths (SSSP) problem asks for the maintenance of approximate distances from a dedicated source $s$ while optimizing the total time…
We consider the distributed and parallel construction of low-diameter decompositions with strong diameter for (weighted) graphs and (weighted) graphs that can be separated through $k \in \tilde{O}(1)$ shortest paths. This class of graphs…
A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…
We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is…
Single Source Shortest Paths ($\textrm{SSSP}$) is among the most well-studied problems in computer science. In the incremental (resp. decremental) setting, the goal is to maintain distances from a fixed source in a graph undergoing edge…
In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
In this paper, we study the problem of approximating the minimum cut in a distributed message-passing model, the CONGEST model. The minimum cut problem has been well-studied in the context of centralized algorithms. However, there were no…
This paper presents parallel, distributed and quantum algorithms for single-source shortest paths when edges can have negative weights (negative-weight SSSP). We show a framework that reduces negative-weight SSSP in all these setting to…