Related papers: Distributed Computation of Mixing Time
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…
Unlike conventional "black-box" transformers with classical self-attention mechanism, we build a lightweight and interpretable transformer-like neural net by unrolling a mixed-graph-based optimization algorithm to forecast traffic with…
Consider the setting where each vertex of a graph has a function, and communications can only occur between vertices connected by an edge. We wish to minimize the sum of these functions. For the case when each function is the sum of a…
Efficient and robust algorithms for decentralized estimation in networks are essential to many distributed systems. Whereas distributed estimation of sample mean statistics has been the subject of a good deal of attention, computation of…
The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among…
Graphlet analysis is an approach to network analysis that is particularly popular in bioinformatics. We show how to set up a system of linear equations that relate the orbit counts and can be used in an algorithm that is significantly…
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph $G$ over $n$ nodes that…
Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
We consider distributed iterative algorithms for the averaging problem over time-varying topologies. Our focus is on the convergence time of such algorithms when complete (unquantized) information is available, and on the degradation of…
Kemeny's constant for random walks on a graph is defined as the mean hitting time from one node to another selected randomly according to the stationary distribution. It has found numerous applications and attracted considerable research…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…
We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a…
This paper proposes a novel class of distributed continuous-time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents. We establish the…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…
Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…