Human navigation has been a topic of interest in spatial cognition from the past few decades. It has been experimentally observed that humans accomplish the task of way-finding a destination in an unknown environment by recognizing landmarks. Investigations using network analytic techniques reveal that humans, when asked to way-find their destination, learn the top ranked nodes of a network. In this paper we report a study simulating the strategy used by humans to recognize the centers of a network. We show that the paths obtained from our simulation has the same properties as the paths obtained in human based experiment. The simulation thus performed leads to a novel way of path-finding in a network. We discuss the performance of our method and compare it with the existing techniques to find a path between a pair of nodes in a network.
A rigorous graph theory based approach to path finding strategy was proposed by , @cite_15 . They provide a method of navigation based on vertex labeling. They establish a labeling strategy for the vertices of a graph in a way that allows one to compute the distance between any two vertices directly from the labels, without using any additional information about the network.
@cite_15
63325702 2112513979 2964124596 1978145399
We consider vertex-labeled graphs, where each vertex v is attached with a label from a set of labels. The vertex-to-label distance query desires the length of the shortest path from the given vertex to the set of vertices with the given label. We show how to construct an oracle for a vertex-labeled planar graph, such that (O( 1 n n) ) storing space is needed, and any vertex-to-label query can be answered in (O( 1 n ) ) time with stretch 1 + e. Here, Δ is the hop-diameter of the given graph. For the case that Δ = O(logn), we construct a distance oracle that achieves (O( 1 n) ) query time, without changing space usage. [SODA 2010] have recently presented a theoretical analysis of several practical point-to-point shortest path algorithms based on modeling road networks as graphs with low highway dimension. They also analyze a labeling algorithm. While no practical implementation of this algorithm existed, it has the best time bounds. This paper describes an implementation of the labeling algorithm that is faster than any existing method on continental road networks. The goal of a hub-based distance labeling scheme for a network G = (V, E) is to assign a small subset S(u) ⊆ V to each node u ∈ V, in such a way that for any pair of nodes u, v, the intersection of hub sets S(u) ∩ S(v) contains a node on the shortest uv-path. The existence of small hub sets, and consequently efficient shortest path processing algorithms, for road networks is an empirical observation. A theoretical explanation for this phenomenon was proposed by (SODA 2010) through a network parameter they called highway dimension, which captures the size of a hitting set for a collection of shortest paths of length at least r intersecting a given ball of radius 2r. In this work, we revisit this explanation, introducing a more tractable (and directly comparable) parameter based solely on the structure of shortest-path spanning trees, which we call skeleton dimension. We show that skeleton dimension admits an intuitive definition for both directed and undirected graphs, provides a way of computing labels more efficiently than by using highway dimension, and leads to comparable or stronger theoretical bounds on hub set size. A distance labeling scheme is a distributed data-structure designed to answer queries about distance between any two vertices of a graph G. The data-structure consists in a label L(x,G) assigned to each vertex x of G such that the distance d"G(x,y) between any two vertices x and y can be estimated as a function f(L(x,G),L(y,G)). In this paper, by the use of split decomposition of graphs, we combine several types of distance labeling schemes. This yields to optimal label length schemes for the family of distance-hereditary graphs and for other families of graphs, allowing distance estimation in constant time once the labels have been constructed.