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We consider the random interlacements process with intensity $u$ on ${\mathbb Z}^d$, $d\ge 5$ (call it $I^u$), built from a Poisson point process on the space of doubly infinite nearest neighbor trajectories on ${\mathbb Z}^d$. For $k\ge 3$…

Probability · Mathematics 2012-07-05 Hubert Lacoin , Johan Tykesson

We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $poly(\log{\log{n}})$ rounds in the near-linear memory MPC model. Our results are for…

Data Structures and Algorithms · Computer Science 2025-05-20 Michal Dory , Shaked Matar

Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…

Databases · Computer Science 2021-10-20 Chris Conlan , Teddy Cunningham , Gunduz Vehbi Demirci , Hakan Ferhatosmanoglu

This article considers two variants of a shortest path problem for a car-like robot visiting a set of waypoints. The sequence of waypoints to be visited is specified in the first variant while the robot is allowed to visit the waypoints in…

Robotics · Computer Science 2018-09-12 Sivakumar Rathinam , Satyanarayana Gupta Manyam , Yuntao Zhang

We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…

Data Structures and Algorithms · Computer Science 2020-03-09 Michal Dory , Merav Parter

We consider single-source shortest path algorithms that perform a sequence of relaxation steps whose ordering depends only on the input graph structure and not on its weights or the results of prior steps. Each step examines one edge of the…

Data Structures and Algorithms · Computer Science 2023-05-17 David Eppstein

We consider a variant of two-point Euclidean shortest path query problem: given a polygonal domain, build a data structure for two-point shortest path query, provided that query points always lie on the boundary of the domain. As a main…

Computational Geometry · Computer Science 2009-11-30 Sang Won Bae , Yoshio Okamoto

We give an algorithm that takes a directed graph $G$ undergoing $m$ edge insertions with lengths in $[1, W]$, and maintains $(1+\epsilon)$-approximate shortest path distances from a fixed source $s$ to all other vertices. The algorithm is…

Data Structures and Algorithms · Computer Science 2025-06-25 Yang P. Liu

Many state-of-the-art Segment Routing (SR) Traffic Engineering (TE) algorithms rely on Linear Program (LP)-based optimization. However, the poor scalability of the latter and the resulting high computation times impose severe restrictions…

Networking and Internet Architecture · Computer Science 2024-08-27 Alexander Brundiers , Timmy Schüller , Nils Aschenbruck

We consider a class of point processes (pp), which we call {\em sub-Poisson}; these are pp that can be directionally-convexly ($dcx$) dominated by some Poisson pp. The $dcx$ order has already been shown useful in comparing various point…

Probability · Mathematics 2012-12-05 Bartlomiej Blaszczyszyn , D. Yogeshwaran

In this paper, we present the downlink coverage and rate analysis of a cellular vehicle-to-everything (C-V2X) communication network where the locations of vehicular nodes and road side units (RSUs) are modeled as Cox processes driven by a…

Information Theory · Computer Science 2019-01-29 Vishnu Vardhan Chetlur , Harpreet S. Dhillon

Computing shortest paths is a fundamental primitive for several social network applications including socially-sensitive ranking, location-aware search, social auctions and social network privacy. Since these applications compute paths in…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-09-05 Rachit Agarwal , Matthew Caesar , P. Brighten Godfrey , Ben Y. Zhao

The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a…

Probability · Mathematics 2017-09-19 Martin Dirrler , Martin Schlather

Given a set $\mathcal{P}$ of $h$ pairwise disjoint simple polygonal obstacles in $\mathbb{R}^2$ defined with $n$ vertices, we compute a sketch $\Omega$ of $\mathcal{P}$ whose size is independent of $n$, depending only on $h$ and the input…

Computational Geometry · Computer Science 2019-09-17 R Inkulu , Sanjiv Kapoor

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered…

Disordered Systems and Neural Networks · Physics 2009-10-31 Cristian F. Moukarzel

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…

Information Theory · Computer Science 2015-10-13 Sudarshan Guruacharya , Hina Tabassum , Ekram Hossain

Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.

Probability · Mathematics 2023-09-06 Vladimir I. Piterbarg

We reduce the problem of computing a rectilinear shortest path between two given points s and t in the splinegonal domain \calS to the problem of computing a rectilinear shortest path between two points in the polygonal domain. As part of…

Computational Geometry · Computer Science 2017-12-12 Tameem Choudhury , R. Inkulu

Shortest path problems are a touchstone for evaluating the computing performance and functional range of novel computing substrates. Much has been published in recent years regarding the use of biocomputers to solve minimal path problems…

Emerging Technologies · Computer Science 2019-05-14 Richard Mayne

Poisson's equation has a lot of applications in various areas. Usually it is hard to derive the explicit expression of the solution of Poisson's equation for a Markov chain on an infinitely many state space. We will present a computational…

Probability · Mathematics 2021-01-05 Jinpeng Liu , Yuanyuan Liu , Yiqiang Q. Zhao