Energy of Convex Sets, Shortest Paths, and Resistance

A New Algorithm for the Discrete Shortest Path Problem in a Network Based on Ideal Fuzzy Sets

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for ...

Convex p-partitions of bipartite graphs

A set of vertices X of a graph G is convex if it contains all vertices on shortest paths between vertices of X. We prove that for fixed p ≥ 1, all partitions of the vertex set of a bipartite graph into p convex sets can be found in polynomial time.

Compromise-free Pathfinding on a Navigation Mesh

We want to compute geometric shortest paths in a collection of convex traversable polygons, also known as a navigation mesh. Simple to compute and easy to update, navigation meshes are widely used for pathfinding in computer games. When the mesh is static, shortest path problems can be solved exactly and very fast but only after a costly preprocessing step. When the mesh is dynamic, practitione...

Functionally closed sets and functionally convex sets in real Banach spaces

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

Shortest paths in convex and simple weighted polygons