In this paper, we present an algorithm for exploring an unknown graph with opaque edges by multiple robots. We show that this algorithm is near optimal on graphs with n vertices and superlinear number of edges (i.e., ω(n) edges), and give an adversarial construction to show that the algorithm does not perform well on cyclic graphs with O(n) edges.

In this paper, we present an algorithm for the exploration of an unknown graph by multiple robots, which is never worse than depth-first search with a single robot. On trees, we prove that the algorithm is optimal for two robots. For k robots, the algorithm has an optimal dependence on the size of the tree but not on its radius. We believe that the algorithm performs well on any tree, and this is substantiated by simulations. For trees with e edges and radius r, the exploration time is less than 2e/k + (1 + (k/r))k-1(2/k!)rk-1= (2e/k) + O((k + r)k-1) (for r >; k,k-1), thereby improving a recent method with time O((e/logk) + r) [2], and almost reaching the lower bound max((2e/k), 2r). The model underlying undirected-graph exploration is a set of rooms connected by opaque passages; thus, the algorithm is appropriate for scenarios like indoor navigation or cave exploration. In this framework, communication can be realized by bookkeeping devices being dropped by the robots at explored vertices, the states of which are read and changed by further visiting robots. Simulations have been performed in both tree and graph explorations to corroborate the mathematical results.

In this paper we study the problem of multi-robot exploration of unknown indoor environments that are modeled as trees. Specifically, our approach consider that robots deploy and communicate with active landmarks in every intersection they encounter. We present a novel algorithm that is guaranteed to completely explore any tree with m edges and diameter D, by allowing k robots to be fed into the tree one at a time. We prove that the exploration time of the algorithm grows in linear proportion with the size of the tree and is not bigger than D+m. Simulation results are presented that corroborate the theoretical analysis.

In this paper we present an algorithm for the exploration of an unknown graph with k robots, which is guaranteed to succeed on any graph, and which on trees we prove to be near-optimal for two robots, having optimal dependence on the size of the tree but not on its radius. We believe that the algorithm performs well on any graph, and this is substantiated by simulations. For trees with n edges and radius r, the exploration time is 2n/k + O(rk-1), improving a recent method with O(n/log k + r) [1], and almost reaching the lower bound max (2n/k, 2r). The algorithm is meant to be used in indoor navigation or cave search scenarios where the environment can be modeled as a graph. In this scenario, communication is realized by the devices being dropped by the robots at explored vertices, and the states of which are read and changed by further visiting robots. Simulations on Player/Stage platform have been performed in both tree and graph exploration which corroborate the mathematical results.

In this article we analyze the capabilities of various models of sensor networks with the Boolean sensing model for mobile or stationary sensors and targets, under random or optimal placement, independent or globally coordinated search, and stealthy or visible sensors. For each model we give an upper bound for the capabilities under any strategy, and a search strategy which at least asymptotically matches that bound. To ensure comparability of these models, we present them using the same parameters: the sensing radius r , sensor placement density λ, as well as the travel distance l of each sensor and d of the target. By this we obtain a complete analysis of the geometric coverage and detection capabilities of the various models of sensor networks, where we abstract from issues like communication and power management.

Previous work on the coverage of mobile sensor networks focuses on algorithms to reposition sensors in order to achieve a static configuration with an enlarged covered area. In this paper, we study the dynamic aspects of the coverage of a mobile sensor network that depend on the process of sensor movement. As time goes by, a position is more likely to be covered; targets that might never be detected in a stationary sensor network can now be detected by moving sensors. We characterize the area coverage at specific time instants and during time intervals, as well as the time it takes to detect a randomly located stationary target. Our results show that sensor mobility can be exploited to compensate for the lack of sensors and improve network coverage. For mobile targets, we take a game theoretic approach and derive optimal mobility strategies for sensors and targets from their own perspectives.

In this paper it is shown that for any set of n points selected from the d-dimensional unit cube, d odd, the volume of the smallest simplex spanned by the set is $O(n^{-(1+{1\over 2d})})$, which is a slight improvement on the only known upper bound O(n -1 )$, although still far from the lower bound $\Omega(n^{-d}\log n)$.

We prove that planar pseudotriangulations have realizations as polyhedral surfaces in three-space. Two main implications are presented. The spatial embedding leads to a novel flip operation that allows for a drastic reduction of flip distances, especially between (full) triangulations. Moreover, several key results for triangulations, like flipping to optimality, (constrained) Delaunayhood, and a convex polytope representation, are extended to pseudotriangulations in a natural way.

This paper presents an algorithm that tests the congruence of two sets ofn points in d-dimensional space in o(nr½ d] log n) time.This improves the previous best algorithm for dimensions d > 6.