Shortest path can be computed in real-time for single navigational instructions. However, complex optimisation tasks, lots of travel-distances (lengths shortest paths) are needed and the total workload becomes a burden. We present fast method estimating travel-distance from one location to another by using an overhead graph that stores ratio between bird-distance few representative locations. T...

For a given graph G, the square of G, denoted by G2, is a graph with the vertex set V(G) such that two vertices are adjacent if and only if the distance of these vertices in G is at most two. A graph G is called squared if there exists some graph H such that G= H2. A function f:V(G) {0,1,2…, k} is called a coloring of G if for every pair of vertices x,yV(G) with d(x,y)=1 we have |f(x)-f(y)|2 an...