Related papers: Fast Deterministic Constructions of Linear-Size Sp…
We study a $(1+\epsilon)$-approximate single-source shortest paths (henceforth, $(1+\epsilon)$-SSSP) in $n$-vertex undirected, weighted graphs in the parallel (PRAM) model of computation. A randomized algorithm with polylogarithmic time and…
This paper presents new deterministic and distributed low-diameter decomposition algorithms for weighted graphs. In particular, we show that if one can efficiently compute approximate distances in a parallel or a distributed setting, one…
A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy…
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…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. --…
We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with…
We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…
This paper addresses the cornerstone family of \emph{local problems} in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in…
This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems.…
We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here $n$ is the number of nodes in the…
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…
We present the first polynomial time algorithm for the f vertex fault tolerant spanner problem, which achieves almost optimal spanner size. Our algorithm for constructing f vertex fault tolerant spanner takes $O(k\cdot n\cdot m^2 \cdot W)$…
Additive spanners are fundamental graph structures with wide applications in network design, graph sparsification, and distance approximation. In particular, a $4$-additive spanner is a subgraph that preserves all pairwise distances up to…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…
The Signal-to-Interference-and-Noise-Ratio (SINR) physical model is one of the legitimate models of wireless networks. Despite of the vast amount of study done in design and analysis of centralized algorithms supporting wireless…
We present new deterministic algorithms for computing distributed weighted minimum weight cycle (MWC) in undirected and directed graphs and distributed weighted all nodes shortest cycle (ANSC) in directed graphs. Our algorithms for these…
We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D \cdot \log n \cdot\log^2\Delta)$ rounds in the \CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $\Delta$ the…
There is a recent exciting line of work in distributed graph algorithms in the $\mathsf{CONGEST}$ model that exploit expanders. All these algorithms so far are based on two tools: expander decomposition and expander routing. An…