Related papers: Robust Lower Bounds for Graph Problems in the Blac…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
In this paper we prove lower bounds on randomized multiparty communication complexity, both in the \emph{blackboard model} (where each message is written on a blackboard for all players to see) and (mainly) in the \emph{message-passing…
We consider the problem of finding a maximal independent set (MIS) in the shared blackboard communication model with vertex-partitioned inputs. There are $n$ players corresponding to vertices of an undirected graph, and each player sees the…
Motivated by the increasing need to understand the distributed algorithmic foundations of large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where $k \geq 2$…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
We consider the point-to-point message passing model of communication in which there are $k$ processors with individual private inputs, each $n$-bit long. Each processor is located at the node of an underlying undirected graph and has…
In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…
In this paper, we consider the problem of clustering graph nodes and sparsifying graph edges over distributed graphs, when graph edges with possibly edge duplicates are observed at physically remote sites. Although edge duplicates across…
A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…
We propose a linear algebraic method, rooted in the spectral properties of graphs, that can be used to prove lower bounds in communication complexity. Our proof technique effectively marries spectral bounds with information-theoretic…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
We study the communication complexity of the Minimum Vertex Cover (MVC) problem on general graphs within the \(k\)-party one-way communication model. Edges of an arbitrary \(n\)-vertex graph are distributed among \(k\) parties. The…
We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose…
We study the $k$-edge connectivity problem on undirected graphs in the distributed sketching model, where we have $n$ nodes and a referee. Each node sends a single message to the referee based on its 1-hop neighborhood in the graph, and the…
Graph spanners are sparse subgraphs which approximately preserve all pairwise shortest-path distances in an input graph. The notion of approximation can be additive, multiplicative, or both, and many variants of this problem have been…
We study the communication complexity of a number of graph properties where the edges of the graph $G$ are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are: * An Omega(n) lower bound…
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 load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…