Graph-like Representation Research Articles

Route selection in non-Euclidean virtual environments.

The way people choose routes through unfamiliar environments provides clues about the underlying representation they use. One way to test the nature of observers' representation is to manipulate the structure of the scene as they move through it and measure which aspects of performance are significantly affected and which are not. We recorded the routes that participants took in virtual mazes to reach previously-viewed targets. The mazes were either physically realizable or impossible (the latter contained 'wormholes' that altered the layout of the scene without any visible change at that moment). We found that participants could usually find the shortest route between remembered objects even in physically impossible environments, despite the gross failures in pointing that an earlier study showed are evident in the physically impossible environment. In the physically impossible conditions, the choice made at a junction was influenced to a greater extent by whether that choice had, in the past, led to the discovery of a target (compared to a shortest-distance prediction). In the physically realizable mazes, on the other hand, junction choices were determined more by the shortest distance to the target. This pattern of results is compatible with the idea of a graph-like representation of space that can include information about previous success or failure for traversing each edge and also information about the distance between nodes. Our results suggest that complexity of the maze may dictate which of these is more important in influencing navigational choices.

A Graph-like Neural Representation of Indoor Spaces Revealed Using fMRI

A Graph-like Neural Representation of Indoor Spaces Revealed Using fMRI

When reactive agents are not enough: Tactical level decisions in pedestrian simulation

Pedestrian and crowd simulation is generally focused on operational level decisions, providing the choice of exact steps of pedestrians in a representation of the environment, with the aim of replicating observed patterns of space utilization, trajectories and timings. When relatively large environments are considered, though, tactical level decisions become equally important: in general, multiple paths can be followed to reach a target from an entrance or starting point, and path length might not be the only reasonable criterion. This paper presents a hybrid agent architecture for modeling different types of decisions in a pedestrian simulation system, encompassing a floor-field based operational level (based on a “least effort” principle) and an adaptive tactical level component, provided with a graph-like representation of the envornment, considering both perceived congestion and characteristics of potential paths in the related decision. The model is experimented and evaluated both qualitatively and quantitatively in benchmark scenarios to show its adequacy and expressiveness.

Exact Cover with Light

We suggest a new optical solution for solving the YES/NO version of the Exact Cover problem by using the massive parallelism of light. The idea is to build an optical device which can generate all possible solutions of the problem and then to pick the correct one. In our case the device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible covers (exact or not) of the given set. For selecting the correct solution we assign to each item, from the set to be covered, a special integer number. These numbers will actually represent delays induced to light when it passes through arcs. The solution is represented as a subray arriving at a certain moment in the destination node. This will tell us if an exact cover does exist or not.

Solving the subset-sum problem with a light-based device

We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. The nodes are connected by arcs in a special way which lets us to generate all possible subsets of the given set. To each arc we assign either a number from the given set or a predefined constant. When the light is passing through an arc it is delayed by the amount of time indicated by the number placed in that arc. At the destination node we will check if there is a ray whose total delay is equal to the target value of the subset sum problem (plus some constants).

Solving the Hamiltonian path problem with a light-based computer

In this paper we propose a special computational device which uses light rays for solving the Hamiltonian path problem on a directed graph. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes. In each node the rays are uniquely marked so that they can be easily identified. At the destination node we will search only for particular rays that have passed only once through each node. We show that the proposed device can solve small and medium instances of the problem in reasonable time.

Normal forms for answer sets programming

Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the kernel of the program, is useful for studying existence and number of answer sets. A kernel program is composed of the atoms which are undefined in the Well-founded semantics, which are those that directly affect the existence of answer sets. The body of rules is composed of negative literals only. Thus, the kernel form tends to be significantly more compact than other formulations. Also, it is possible to check consistency of kernel programs in terms of colorings of the Extended Dependency Graph program representation which we previously developed. The second normal form is called 3-kernel. A 3-kernel program is composed of the atoms which are undefined in the Well-founded semantics. Rules in 3-kernel programs have at most two conditions, and each rule either belongs to a cycle, or defines a connection between cycles. 3-kernel programs may have positive conditions. The 3-kernel normal form is very useful for the static analysis of program consistency, i.e. the syntactic characterization of existence of answer sets. This result can be obtained thanks to a novel graph-like representation of programs, called Cycle Graph which presented in the companion article Costantini (2004b).

Statistical theory of Internet exploration

The general methodology used to construct Internet maps consists in merging all the discovered paths obtained by sending data packets from a set of active computers to a set of destination hosts, obtaining a graphlike representation of the network. This technique, sometimes referred to as Internet tomography, spurs the issue concerning the statistical reliability of such empirical maps. We tackle this problem by modeling the network sampling process on synthetic graphs and by using a mean-field approximation to obtain expressions for the probability of edge and vertex detection in the sampled graph. This allows a general understanding of the origin of possible sampling biases. In particular, we find a direct dependence of the map statistical accuracy upon the topological properties (in particular, the betweenness centrality property) of the underlying network. In this framework, it appears that statistically heterogeneous network topologies are captured better than the homogeneous ones during the mapping process. Finally, the analytical discussion is complemented with a thorough numerical investigation of simulated mapping strategies in network models with varying topological properties.

Mapping in unknown graph-like worlds

We consider the problem of constructing a map of an unknown environment by an autonomous agent such as a mobile robot. Because accurate positional information is often difficult to ensure, we consider the problem of exploration in the absence of metric (positional) information. Worlds are represented by graphs (not necessarily planar) consisting of a fixed number of discrete places linked by bidirectional paths. We assume the robot can consistently enumerate the edges leaving a vertex (that is, it can assign a cyclic ordering). A mobile robot is assigned the task of creating a topological map, i.e. a graph-like representation of the places in the world and their connectivity, by moving from place to place along the paths it encounters. It can detect edges and count them, but cannot directly sense the labels associated with a place or an edge. In principle, this type of representation could be used for non-spatial environments such as computer networks. We present an approach to the exploration of unknown environments for which local sensing information alone is insufficient to distinguish distinct places, based simply on the structure of the world itself. Places are identified by a non-unique signature and by using a collection of such non-unique local signatures, an extended signature may be constructed that determines the robot's position (although in certain “degenerate” worlds additional information is required). We describe the “exploration tree” as a representation of a collection of alternative descriptions of the environment. In addition, heuristics are presented that can accelerate the search for the correct world model. © 1996 John Wiley & Sons, Inc.