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Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…
In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Robots with very limited capabilities are placed on the vertices of a graph and are required to move toward a single, common vertex, where they remain stationary once they arrive. This task is referred to as the GATHERING problem. Most of…
We study a generalized motion planning problem involving multiple autonomous robots navigating in a $d$-dimensional Euclidean space in the presence of a set of obstacles whose positions are unknown a priori. Each robot is required to visit…
The 1-2-3 Conjecture, introduced by Karo\'nski, {\L}uczak, and Thomason in 2004, was recently solved by Keusch. This implies that, for any connected graph $G$ different from $K_2$, we can turn $G$ into a locally irregular multigraph $M(G)$,…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
This paper studies the multi-robot reliable navigation problem in uncertain topological networks, which aims at maximizing the robot team's on-time arrival probabilities in the face of road network uncertainties. The uncertainty in these…
We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…
Multi-objective or multi-destination path planning is crucial for mobile robotics applications such as mobility as a service, robotics inspection, and electric vehicle charging for long trips. This work proposes an anytime iterative system…
The deterministic random walk is a deterministic process analogous to a random walk. While there are some results on the cover time of the rotor-router model, which is a deterministic random walk corresponding to a simple random walk,…
In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold,…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
This paper considers the Hamiltonian walk problem in the multi-agent coordination framework, referred to as $k$-agents Hamiltonian walk problem ($k$-HWP). In this problem, a set of $k$ connected agents collectively compute a spanning walk…
We introduce a set of techniques that allow for efficiently generating many independent random walks in the Massive Parallel Computation (MPC) model with space per machine strongly sublinear in the number of vertices. In this…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
We define a random walk problem which admits analytic results, on a class of infinite periodic lattices which are directed and colored. Our approach is motivated from the fact that such lattices arise in string theoretic constructs of…