In geographical databases for navigation, users raise various types of queries concerning route guidance. The most fundamental query is a shortest-route query, but, as dynamical traffic information newly becomes available and the static geographical database of roads itself has grown up further, more flexible queries are required to realize a user-friendly interface meeting the current settings...

The maximum detour and spanning ratio of an embedded graph G are values that measure how well G approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe O(n logn) time algorithms for computing the maximum detour and spanning ratio of a planar polygonal path. These algorithms solve open problems posed in at least two previous works [5,10]. We also ge...

Restricted detour distance between two vertices and of a graph is the length longest u- v path for induced condition (V (P))=P. The restricted polynomial depends on denoted by D*(G,x) defined = ∑{u,v}xD*(u,v) where summation taken over all unordered pairs (u,v) distinct u V(G). In this paper, we investigate straight chain wheel graphs φ(WkB) compute index φ(WkB).

The detour distance between two vertices u and v in a connected graph G is the length of a longest v u − path in G. We survey results and some open questions on detour distance, including connections of this distance to domination, coloring and Hamiltonian properties of graphs.

The DETOUR System is a novel percutaneous femoropopliteal bypass-like procedure for PAD patients with complex disease including long lesions, heavy calcification, and chronic total occlusions. Detour system uses standard endovascular techniques crossing device stent graft to create bypass. We report two-year safety effectiveness results of this innovative revascularization. DETOUR-2 IDE study p...

We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. A...