Related papers: Efficiently navigating a random Delaunay triangula…
Ground robots navigating in complex, dynamic environments must compute collision-free trajectories to avoid obstacles safely and efficiently. Nonconvex optimization is a popular method to compute a trajectory in real-time. However, these…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
We study the problem of approximately simulating a $t$-step random walk on a graph where the input edges come from a single-pass stream. The straightforward algorithm using reservoir sampling needs $O(nt)$ words of memory. We show that this…
A major challenge with off-road autonomous navigation is the lack of maps or road markings that can be used to plan a path for autonomous robots. Classical path planning methods mostly assume a perfectly known environment without accounting…
We study in-network computation on general network topologies. Specifically, we are given the description of a function, and a network with distinct nodes at which the operands of the function are made available, and a designated sink where…
Quantum random walks on graphs have been shown to display many interesting properties, including exponentially fast hitting times when compared with their classical counterparts. However, it is still unclear how to use these novel…
We propose a simple and time-optimal algorithm for property testing a graph for its conductance in the CONGEST model. Our algorithm takes only $O(\log n)$ rounds of communication (which is known to be optimal), and consists of simply…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
In this paper, we study a facility location problem within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple constraints such as a…
We present new quantum algorithms for Triangle Finding improving its best previously known quantum query complexities for both dense and spare instances.For dense graphs on $n$ vertices, we get a query complexity of $O(n^{5/4})$ without any…
We consider the problem of finding minimum-link rectilinear paths in rectilinear polygonal domains in the plane. A path or a polygon is rectilinear if all its edges are axis-parallel. Given a set $\mathcal{P}$ of $h$ pairwise-disjoint…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random…
We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of the map in positive speed and that the return probability to…
We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…