Related papers: Minimum-weight combinatorial structures under rand…
We study the problem of sketching an input graph, so that given the sketch, one can estimate the weight of any cut in the graph within factor $1+\epsilon$. We present lower and upper bounds on the size of a randomized sketch, focusing on…
In length-constrained minimum spanning tree (MST) we are given an $n$-node graph $G = (V,E)$ with edge weights $w : E \to \mathbb{Z}_{\geq 0}$ and edge lengths $l: E \to \mathbb{Z}_{\geq 0}$ along with a root node $r \in V$ and a…
We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…
An algorithm is proposed for constructing directed spanning forests of the minimum weight, in which the maximum possible degree of affinity between the minimum forests is preserved when the number of trees changes. The correctness of the…
For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
Consider the complete n-vertex graph whose edge-lengths are independent exponentially distributed random variables. Simultaneously for each pair of vertices, put a constant flow between them along the shortest path. Each edge gets some…
Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
A solution of the $k$ shortest paths problem may output paths that are identical up to a single edge. On the other hand, a solution of the $k$ independent shortest paths problem consists of paths that share neither an edge nor an…
In this paper, we consider the problem of tuning the edge weights of a networked system described by linear time-invariant dynamics. We assume that the topology of the underlying network is fixed and that the set of feasible edge weights is…
Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a…
We study the structure of the load-based spanning tree (LST) that carries the maximum weight of the Erdos-Renyi (ER) random network. The weight of an edge is given by the edge-betweenness centrality, the effective number of shortest paths…
An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$…
The inference of minimum spanning arborescences within a set of objects is a general problem which translates into numerous application-specific unsupervised learning tasks. We introduce a unified and generic structure called edit…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of…
For a simple (unbiased) random walk on a connected graph with $n$ vertices, the cover time (the expected number of steps it takes to visit all vertices) is at most $O(n^3)$. We consider locally biased random walks, in which the probability…