Related papers: Shortest paths on systems with power-law distribut…

Let $(M,g_1)$ be a complete $d$-dimensional Riemannian manifold for $d > 1$. Let $\mathcal X_n$ be a set of $n$ sample points in $M$ drawn randomly from a smooth Lebesgue density $f$ supported in $M$. Let $x,y$ be two points in $M$. We…

This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…

Many stochastic time series can be modelled by discrete random walks in which a step of random sign but constant length $\delta x$ is performed after each time interval $\delta t$. In correlated discrete time random walks (CDTRWs), the…

We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…

We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability $P(l)$ of generating a loop of perimeter $l$ is expressible in terms of the…

Small-world networks (SWN), obtained by randomly adding to a regular structure additional links (AL), are of current interest. In this article we explore (based on physical models) a new variant of SWN, in which the probability of realizing…

This paper studies approximation by shallow ReLU$^s$ networks, $\sigma_s(t)=\max\{0,t\}^s$, together with their generalization behavior under $\ell_1$ path-norm control. For the $L^p$-type integral spaces…

We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of $N$ nodes of degree $c \ge 3$. Starting from a random initial node at time $t=0$, at each time…

We consider the randomized communication complexity of the distributed $\ell_p$-regression problem in the coordinator model, for $p\in (0,2]$. In this problem, there is a coordinator and $s$ servers. The $i$-th server receives $A^i\in\{-M,…

We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional ($d=2$) square lattices to be improved by the…

The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding…

We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree $k$ is proportional to $k^{\alpha}$, where $\alpha$ is a tuning parameter. We study both numerically and analytically three…

In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental…

Motivated by multi-domain service function chain (SFC) orchestration, we define the shortest-longest path (SLP) problem, prove its hardness, and design an efficient fully polynomial time approximation scheme (FPTAS) using the dynamic…

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…

This paper studies Random and Evolving Apollonian networks (RANs and EANs), in d dimension for any d>=2, i.e. dynamically evolving random d dimensional simplices looked as graphs inside an initial d-dimensional simplex. We determine the…

We consider random singlet phases of spin-$\frac{1}{2}$, random, antiferromagnetic spin chains, in which the universal leading-order divergence $\frac{\ln 2}{3}\ln\ell$ of the average entanglement entropy of a block of $\ell$ spins, as well…

Higher order clustering coefficients $C(x)$ are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex $i$ equals $x$, when one neglects all…

Shortest paths problems are subject to extensive studies in classic distributed models such as the CONGEST or Congested Clique. These models dictate how nodes may communicate in order to determine shortest paths in a distributed input…

Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…