In 1984, Matthews and Sumner conjectured that every 4-connected, claw-free graph contains a Hamiltonian cycle. This still unresolved conjecture has been the motivation for research into the existence of other cycle structures. In this paper, we consider the stronger property of pancyclicity for 4-connected graphs. In particular, we show that every 4-connected, { K 1 , 3 , N ( i , j , k ) }-free graph, where i , j , k ≥ 1 and i + j + k = 6, is pancyclic. This, together with results by Ferrara, Morris, Wenger, and Ferrara et al. completes a characterization of the graphs Y such that every { K 1 , 3 , Y }-free graph is pancyclic. In addition, this represents the best known progress towards answering a question of Gould concerning a characterization of the pairs of forbidden subgraphs that imply pancyclicity in 4-connected graphs.

This paper is not about the details of yet another robot control system, but rather the issues surrounding real-world robotic implementation. It is a fact that in order to realize a future where robots coexist with people in everyday places, we have to pass through a developmental phase that involves some risk. Putting a “Keep Out, Experiment in Progress” sign on the door is no longer possible, since we are now at a level of capability that requires testing over long periods of time in complex realistic environments that contain people. We all know that controlling the risk is important-a serious accident could set the field back globally-but just as important is convincing others that the risks are known and controlled. In this paper, we describe our experience going down this path and we show that mobile robotics research health and safety assessment is still unexplored territory in universities and is often ignored. We hope that this paper will make robotics research labs in universities around the world take note of these issues rather than operating under the radar to prevent any catastrophic accidents.

In this paper, we consider conditions that ensure a hamiltonian graph has a 2-factor with exactly k cycles. Brandt et al. proved that if G is a graph on n >= 4k vertices with minimum degree at least n/2, then G contains a 2-factor with exactly k cycles; moreover this is best possible. Faudree et al. asked if there is some c < 1/2 such that delta(G) >= cn would imply the existence of a 2-factor with k-cycles under the additional hypothesis that G was hamiltonian. This question was answered in the affirmative by Sarkozy, who used the regularity-blow-up method to show that there exists some epsilon > 0 such that for every k >= 1 and large n, 6(G) > ( 8) n suffices.We improve on this result, giving an elementary proof that for every epsilon > 0 and k >= 1, if G is a hamiltonian graph on n >= 3k/epsilon vertices with delta(G) >= (1/2 - epsilon) n, then G contains a 2-factor with k cycles. (C) 2013 Elsevier B.V. All rights reserved.

This paper presents a novel method to rank map hypotheses by the quality of localization they afford. The highest ranked hypothesis at any moment becomes the active representation that is used to guide the robot to its goal location. A single static representation is insufficient for navigation in dynamic environments where paths can be blocked periodically, a common scenario which poses significant challenges for typical planners. In our approach we simultaneously rank multiple map hypotheses by the influence that localization in each of them has on locally accurate odometry. This is done online for the current locally accurate window by formulating a factor graph of odometry relaxed by localization constraints. Comparison of the resulting perturbed odometry of each hypothesis with the original odometry yields a score that can be used to rank map hypotheses by their utility. We deploy the proposed approach on a real robot navigating a structurally noisy office environment. The configuration of the environment is physically altered outside the robots sensory horizon during navigation tasks to demonstrate the proposed approach of hypothesis selection.

A 2-factor in a graph is a spanning 2-regular subgraph, or equivalently a spanning collection of disjoint cycles. In this paper we investigate the existence of 2-factors with a bounded number of odd cycles in a graph. We extend results of Ryjáček, Saito, and Schelp (1999) and show that the number of odd components of a 2-factor in a claw-free graph is stable under Ryjáček’s closure operation. We also consider conditions that ensure the existence of a pair of disjoint 1-factors in a claw-free graph, as the union of such a pair is a 2-factor with no odd cycles.

This paper presents a method to enable a mobile robot working in non-stationary environments to plan its path and localize within multiple map hypotheses simultaneously. The maps are generated using a long-term and short-term memory mechanism that ensures only persistent configurations in the environment are selected to create the maps. In order to evaluate the proposed method, experimentation is conducted in an office environment. Compared to navigation systems that use only one map, our system produces superior path planning and navigation in a non-stationary environment where paths can be blocked periodically, a common scenario which poses significant challenges for typical planners.

This paper presents an account of an autonomous mobile robot deployment in a densely crowded public event with thousands of people from different age groups attending. The robot operated for eight hours on an open floor surrounded by tables, chairs and massive touchscreen displays. Due to the large number of people who were in close vicinity of the robot, different safety measures were implemented including the use of no-go zones which prevent the robot from blocking emergency exits or moving too close to the display screens. The paper presents the lessons learnt and experiences obtained from this experiment, and provides a discussion about the state of mobile service robots in such crowded environments.

This paper presents a mapping and navigation system for a mobile robot, which uses vision as its sole sensor modality. The system enables the robot to navigate autonomously, plan paths and avoid obstacles using a vision based topometric map of its environment. The map consists of a globally-consistent pose-graph with a local 3D point cloud attached to each of its nodes. These point clouds are used for direction independent loop closure and to dynamically generate 2D metric maps for locally optimal path planning. Using this locally semi-continuous metric space, the robot performs shortest path planning instead of following the nodes of the graph - as is done with most other vision-only navigation approaches. The system exploits the local accuracy of visual odometry in creating local metric maps, and uses pose graph SLAM, visual appearance-based place recognition and point clouds registration to create the topometric map. The ability of the framework to sustain vision-only navigation is validated experimentally, and the system is provided as open-source software.

Let D be a directed graph of order n. An anti-directed (hamiltonian) cycle H in D is a (hamiltonian) cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. In this paper we give sufficient conditions for the existence of anti-directed hamiltonian cycles. Specifically, we prove that a directed graph D of even order n with minimum indegree and outdegree greater than \({\frac{1}{2}n + 7\sqrt{n}/3}\) contains an anti-directed hamiltonian cycle. In addition, we show that D contains anti-directed cycles of all possible (even) lengths when n is sufficiently large and has minimum in- and out-degree at least \({(1/2+ \epsilon)n}\) for any \({\epsilon > 0}\) .

A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V(G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pairs of forbidden subgraphs, [J Graph Theory 47 (2004), 183202].

Odometry is an important input to robot navigation systems, and we are interested in the performance of vision-only techniques. In this paper we experimentally evaluate and compare the performance of wheel odometry, monocular feature-based visual odometry, monocular patch-based visual odometry, and a technique that fuses wheel odometry and visual odometry, on a mobile robot operating in a typical indoor environment.

In this paper we present a real-time foreground-background segmentation algorithm that exploits the following observation (very often satisfied by a static camera positioned high in its environment). If a blob moves on a pixel p that had not changed its colour significantly for a few frames, then p was probably part of the background when its colour was static. With this information we are able to update differentially pixels believed to be background. This work is relevant to autonomous minirobots, as they often navigate in buildings where smart surveillance cameras could communicate wirelessly with them. A by-product of the proposed system is a mask of the image regions which are demonstrably background. Statistically significant tests show that the proposed method has a better precision and recall rates than the state of the art foreground/background segmentation algorithm of the OpenCV computer vision library.

Ancillary texts—handbooks, companions, and guides—are the academicpublishing flavor of the moment. In an industry where the words “essay collection” mean the kiss of death, editors package essay collections as ancillary—and indispensable—to a primary text. A Historical Guide to Emily Dickinson is such a collection. I’m not sure how useful it will be to new students of the poet, but this collection edited by Vivian Pollak compensates by offering a generous selection of essays by and for Dickinson scholars. Emily Dickinson, as several of the contributors to the Historical Guide note, has often been considered extraneous to history. Yet her father was a civic leader and politician. She knew many important figures in political, intellectual, and literary New England, and the fact that some of them (Samuel Bowles, T.W. Higginson, Josiah Holland) have become footnotes to Dickinson doesn’t diminish their centrality to their culture. Reading this Guide one is impressed by the range of public issues that Dickinson addressed in her private writing. There are good basic pieces in the collection. Vivian Pollak and Marianne Noble’s strong biographical essay tells the story somewhat slant to avoid dull chronology. (There is a point-by-point illustrated chronology later in the book, obviating the need for a step-by-step narrative.) Jonathan Morse’s “Bibliographical Essay” is an energetically told, succinct publishing history. Impressive too is Jane Donahue Eberwein’s careful look at contexts for Dickinson in 19th-century religious history.