12429864
Geometric Robot Mapping
The purpose of this paper is to present a technique to create a global map of a robot's surrounding by converting the raw data acquired from a scanning sensor to a compact map composed of just a few generalized polylines (polygonal curves). To merge a new scan with a previously computed map of the surrounding we use an approach that is composed of a local geometric process of merging similar line segments (termed Discrete Segment Evolution) of map and scan with a global statistical control process. The merging process is applied to a dataset gained from a real robot to show its ability to incrementally build a map showing the environment the robot has traveled through.
18161086
Shape-Based Robot Mapping
We present a novel geometric model for robot mapping suited for robots equipped with a laser range finder. The geometric representation is based on shape. Cyclic ordered sets of polygonal lines are the underlying data structures. Specially adapted shape matching techniques originating from computer vision are applied to match range scan against the partially constructed map. Shape matching respects for a wider context than conventional scan matching approaches, allowing to disregard pose estimations. The described shape based approach is an improvement of the underlying geometric models of todays SLAM implementations. Moreover, using our object-centered approach allows for compact representations that are well-suited to bridge the gap from metric information needed in robot motion and path planning to more abstract, i.e. topological or qualitative spatial knowledge desired in complex navigational tasks or communication.
11057176
Wythoff's sequence and N-Heap Wythoff's conjectures
Define a Wythoff's sequence as a sequence of pairs of integers {(A"n,B"n)}"n">"n"""0 such that there exists a finite set of integers T, A"n=mex({A"i,B"i:i
7910466
Computing the unmeasured: an algebraic approach to Internet mapping
Distance estimation is important to many Internet applications. It can aid a World Wide Web client when selecting among several potential candidate servers or among candidate peer-to-peer servers. It can also aid in building efficient overlay or peer-to-peer networks that react dynamically to changes in the underlying Internet. One of the approaches to distance (i.e., time delay) estimation in the Internet is based on placing tracer stations in key locations and conducting measurements between them. The tracers construct an approximated map of the Internet after processing the information obtained from these measurements. This work presents a novel algorithm, based on algebraic tools, that computes additional distances, which are not explicitly measured. As such, the algorithm extracts more information from the same amount of measurement data. Our algorithm has several practical impacts. First, it can reduce the number of tracers and measurements without sacrificing information. Second, our algorithm is able to compute distance estimates between locations where tracers cannot be placed. To evaluate the algorithm's performance, we tested it both on randomly generated topologies and on real Internet measurements. Our results show that the algorithm computes up to 50%-200% additional distances beyond the basic tracer-to-tracer measurements.
5849492
Space lower bounds for distance approximation in the data stream model
(MATH) We consider the problem of approximating the distance of two <i>d</i>-dimensional vectors <b>x</b> and <b>y</b> in the data stream model. In this model, the 2<i>d</i> coordinates are presented as a "stream" of data in some arbitrary order, where each data item includes the index and value of some coordinate and a bit that identifies the vector (<b>x</b> or <b>y</b>) to which it belongs. The goal is to minimize the amount of memory needed to approximate the distance. For the case of <i>L<sup>p</sup></i>-distance with <i>p</i> ε [1,2], there are good approximation algorithms that run in polylogarithmic space in <i>d</i> (here we assume that each coordinate is an integer with <i>O</i>(log <i>d</i>) bits). Here we prove that they do not exist for <i>p</i>ρ2. In particular, we prove an optimal approximation-space tradeoff of approximating <i>L</i><sup>&infty;</sup> distance of two vectors. We show that any randomized algorithm that approximates <i>L</i><sup>&infty;</sup> distance of two length <i>d</i> vectors within factor of <i>d</i><sup>δ</sup> requires ω(<i>d</i><sup>1—4δ</sup>) space. As a consequence we show that for <i>p</i>ρ2/(1—4δ), any randomized algorithm that approximate <i>L</i><sup><i>p</i></sup> distance of two length <i>d</i> vectors within a factor <i>d</i><sup>δ</sup> requires ω(<i>d</i> <sup>1— <sup>2</sup>< \over <sub>p</sub>—4δ</sup>) space.The lower bound follows from a lower bound on the two-party one-round communication complexity of this problem. This lower bound is proved using a combination of information theory and Fourier analysis.
319539
Super-linear time-space tradeoff lower bounds for randomized computation
We prove the first time-space lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by M. Ajtai (1999) in his time-space tradeoffs for deterministic RAM algorithms computing element distinctness and for deterministic Boolean branching programs computing an explicit function based on quadratic forms over GF(2). Our results also give a quantitative improvement over those given by Ajtai. Ajtai shows, for certain specific functions, that any branching program using space S=o(n) requires time T that is superlinear. The functional form of the superlinear bound is not given in his paper, but optimizing the parameters in his arguments gives T= /spl Omega/(n log log n/log log log n) for S=0(n/sup 1-/spl epsiv//). For the same functions considered by Ajtai, we prove a time-space tradeoff of the form T=/spl Omega/(n/spl radic/(log(n/S)/log log(n/S))). In particular for space 0(n/sup 1-/spl epsiv//), this improves the lower bound on time to /spl Omega/(n/spl radic/(log n/log log n)).
12453406
Model-Driven assessment of use cases for dependable systems
Complex real-time systems need to address dependability requirements early on in the development process. This paper presents a model-based approach that allows developers to analyze the dependability of use cases and to discover more reliable and safe ways of designing the interactions with the system and the environment. We use a probabilistic extension of statecharts to model the system requirements. The model is then evaluated analytically based on the success and failure probabilities of events. The analysis may lead to further refinement of the use cases by introducing detection and recovery measures to ensure dependable system interaction. A visual modelling environment for our extended statecharts formalism supporting automatic probability analysis has been implemented in AToM3, A Tool for Multi-formalism and Meta-Modelling. Our approach is illustrated with an elevator control system case study.
17089343
Near-optimal lower bounds on the multi-party communication complexity of set disjointness
We study the communication complexity of the set disjointness problem in the general multiparty model. For t players, each holding a subset of a universe of size n, we establish a near-optimal lower bound of /spl Omega/(n/(t log t)) on the communication complexity of the problem of determining whether their sets are disjoint. In the more restrictive one-way communication model, in which the players are required to speak in a predetermined order, we improve our bound to an optimal /spl Omega/(n/t). These results improve upon the earlier bounds of /spl Omega/(n/t/sup 2/) in the general model, and /spl Omega/((/spl epsiv//sup 2/n)/t/sup 1+/spl epsiv//) in the one-way model, due to Bar-Yossef, Jayram, Kumar, and Sivakumar (2002). As in the case of earlier results, our bounds apply to the unique intersection promise problem. This communication problem is known to have connections with the space complexity of approximating frequency moments in the data stream model. Our results lead to an improved space complexity lower bound of /spl Omega/(n/sup 1-2/k//log n) for approximating the k/sup th/ frequency moment with a constant number of passes over the input, and a technical improvement to /spl Omega/(n/sup 1-2/k/) if only one pass over the input is permitted. Our proofs rely on the information theoretic direct sum decomposition paradigm of Bar-Yossef et al. [2002]. Our improvements stem from novel analytical techniques, as opposed to earlier techniques based on Hellinger and related distances, for estimating the information cost of protocols for one-bit functions.