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Let $G=(V, E)$ be an undirected $n$-vertices $m$-edges graph with non-negative edge weights. In this paper, we present three new algorithms for constructing a $(2k-1)$-stretch distance oracle with $O(n^{1+\frac{1}{k}})$ space. The first…
State-of-the-art emergency navigation approaches are designed to evacuate civilians during a disaster based on real-time decisions using a pre-defined algorithm and live sensory data. Hence, casualties caused by the poor decisions and…
We study the problem of allocating many mobile robots for the execution of a pre-defined sweep schedule in a known two-dimensional environment, with applications toward search and rescue, coverage, surveillance, monitoring, pursuit-evasion,…
An autonomous robot with a limited vision range finds a path to the goal in an unknown environment in 2D avoiding polygonal obstacles. In the process of discovering the environmental map, the robot has to return to some positions marked…
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for every orbit of a rational matrix to escape a compact…
A collection of $k$ mobile agents is arbitrarily deployed in the edges of a directed torus network where agents perpetually move to the successor edge. Each node has a switch that allows one agent of the two incoming edges to pass to its…
Most existing robot formation problems seek a target formation of a certain \emph{minimal} and, thus, efficient structure. Examples include the Gathering and the Chain-Formation problem. In this work, we study formation problems that try to…
In this paper, we solve the local gathering problem of a swarm of $n$ indistinguishable, point-shaped robots on a two dimensional grid in asymptotically optimal time $\mathcal{O}(n)$ in the fully synchronous $\mathcal{FSYNC}$ time model.…
In case of a threat in a public space, the crowd in it should be moved to a shelter or evacuated without delays. Risk management and evacuation planning in public spaces should also take into account uncertainties in the traffic patterns of…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
We propose a space-efficient algorithm for hidden surface removal that combines one of the fastest previous algorithms for that problem with techniques based on bit manipulation. Such techniques had been successfully used in other settings,…
This paper presents a novel control algorithm for robotic manipulators in unstructured environments using proximity sensors partially distributed on the platform. The proposed approach exploits arrays of multi zone Time-of-Flight (ToF)…
A total of more than 3400 public shootings have occurred in the United States between 2016 and 2022. Among these, 25.1% of them took place in an educational institution, 29.4% at the workplace including office buildings, 19.6% in retail…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
Recent papers have shown optimally-competitive on-line strategies for a robot traveling from a point $s$ to a point $t$ in certain unknown geometric environments. We consider the question: Having gained some partial information about the…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
All known algorithms for the Fr\'echet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values.…
In this paper, we consider the problem of deploying a robot from a specification given as a temporal logic statement about some properties satisfied by the regions of a large, partitioned environment. We assume that the robot has noisy…
Emergency navigation algorithms direct evacuees to exits when disastrous events such as fire take place. Due to the spread of hazards, latency in information updating and unstable flows of civilians, emergency evacuation is absolutely a…
The aim of the dispersion problem is to place a set of $k(\leq n)$ mobile robots in the nodes of an unknown graph consisting of $n$ nodes such that in the final configuration each node contains at most one robot, starting from any arbitrary…