This paper proposes a model of adding relations between members of the same level in a pyramid organization structure which is a complete K-ary tree such that the communication of information between every member in the organization becomes the most efficient. When edges between one node and every other node with the same depth N in a complete K-ary tree of height H are added, an optimal depth ...

With the increasing availability of terrain data, e.g., from aerial laser scans, the management of such data is attracting increasing attention in both industry and academia. In particular, spatial queries, e.g., k-nearest neighbor and reverse nearest neighbor queries, in Euclidean and spatial network spaces are being extended to terrains. Such queries all rely on an important operation, that o...

In contrast to classical offline k-k routing, the online packet routing problem allows for an arbitrary number of packets with arbitrary end points and release times. We study this problem on linear array and ring networks. We generalize an earlier result for the offline problem by showing that Farthest First (FF) scheduling is optimal with respect to makespan on linear arrays. We also show tha...

Geometric shortest paths are a major topic in computational geometry; see the survey paper by Mitchell [12]. A shortest path between two points in a simple polygon can be found in linear time using the “funnel” algorithm of Chazelle [3] and Lee and Preparata [10]. A more general problem is to find a shortest path between two points in a polygonal domain. In this case the “rubber band” solution ...

A theorem of Hardy, Littlewood, and Polya, first time is used to find the variational form of the well known shortest path problem, and as a consequence of that theorem, one can find the shortest path problem via quadratic programming. In this paper, we use measure theory to solve this problem. The shortest path problem can be written as an optimal control problem. Then the resulting distribute...

Abstract—This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent such that the communication of information in the organization becomes the most efficient. For a model of adding an edge between a node with a depth M and its descendant with a depth N, we formulated the total shortening di...

Although recent scientific output focuses on multiple shortest-path problem definitions for road networks, none of the existing solutions does efficiently answer all different types of SP queries. This work proposes SALT, a novel framework that not only efficiently answers SP related queries but also k-nearest neighbor queries not handled by previous approaches. Our solution offers all the bene...

Complex networks, such as biological, social, and communication networks, often entail uncertainty, and thus, can be modeled as probabilistic graphs. Similar to the problem of similarity search in standard graphs, a fundamental problem for probabilistic graphs is to efficiently answer k-nearest neighbor queries (k-NN), which is the problem of computing the k closest nodes to some specific node....

For a directed graph G with vertex set V we call a subset C ₵ V a k-(All-) Path Cover if C contains a node from any path consisting of k nodes. This paper considers the problem of constructing small k-Path Covers in the context of road networks with millions of nodes and edges. In many application scenarios the set C and its induced overlay graph constitute a very compact synopsis of G which is...

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the best route choice is not necessarily a path, but rather a time-adaptive strategy that assigns succes...