Related papers: Bounds for Algebraic Gossip on Graphs
We prove that the diameter of threshold (zero temperature) Geometric Inhomogeneous Random Graphs (GIRG) is $\Theta(\log n)$. This has strong implications for the runtime of many distributed protocols on those graphs, which often have…
Although gossip and random walk-based learning algorithms are widely known for decentralized learning, there has been limited theoretical and experimental analysis to understand their relative performance for different graph topologies and…
In earlier work, we showed that it is possible to achieve $O(\log N)$ streaming delay with high probability in a peer-to-peer network, where each peer has as little as four neighbors, while achieving any arbitrary fraction of the maximum…
For an $n$-vertex graph $G$, let $h(G)$ denote the smallest size of a subset of $V(G)$ such that it intersects every maximum independent set of $G$. A conjecture posed by Bollob\'{a}s, Erd\H{o}s and Tuza in early 90s remains widely open,…
In the IoT era, information is more and more frequently picked up by connected smart sensors with increasing, though limited, storage, communication and computation abilities. Whether due to privacy constraints or to the structure of the…
In instances of online kernel learning where little prior information is available and centralized learning is unfeasible, past research has shown that distributed and online multi-kernel learning provides sub-linear regret as long as every…
We give lower bounds for various natural node- and edge-based local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a…
We study different mechanisms of gossip propagation on several network topologies and introduce a new network property, the "spread factor", describing the fraction of neighbors that get to know the gossip. We postulate that for scale-free…
The fundamental theorem of Tur\'{a}n from Extremal Graph Theory determines the exact bound on the number of edges $t_r(n)$ in an $n$-vertex graph that does not contain a clique of size $r+1$. We establish an interesting link between…
Gossip algorithms is a common term to describe protocols for unreliable information dissemination in natural networks, which are not optimally designed for efficient communication between network entities. We consider application of gossip…
In this work we present a new framework for the analysis and design of randomized gossip algorithms for solving the average consensus problem. We show how classical randomized iterative methods for solving linear systems can be interpreted…
The Lov\'{a}sz theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a maximal clique, and so one can instead apply this…
A topological graph is $k$-quasi-planar if it does not contain $k$ pairwise crossing edges. A 20-year-old conjecture asserts that for every fixed $k$, the maximum number of edges in a $k$-quasi-planar graph on $n$ vertices is $O(n)$. Fox…
We prove that any $n$-node graph $G$ with diameter $D$ admits shortcuts with congestion $O(\delta D \log n)$ and dilation $O(\delta D)$, where $\delta$ is the maximum edge-density of any minor of $G$. Our proof is simple, elementary, and…
Given a distribution of pebbles on the vertices of a graph, say that we can pebble a vertex if a pebble is left on it after some sequence of moves, each of which takes two pebbles from some vertex and places one on an adjacent vertex. A…
Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…
We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infinite reduction has a well defined limit allowing us to treat…
In the vertex cover problem, the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every edge of $G$ is incident on at least one vertex in $S$. We study…
In this paper we study gossip networks where a source observing a process sends updates to an underlying graph. Nodes in the graph communicate to their neighbors by randomly sending updates. Our interest is studying the version age of…
By the distributed averaging problem is meant the problem of computing the average value of a set of numbers possessed by the agents in a distributed network using only communication between neighboring agents. Gossiping is a well-known…