Recently, shortest path tree construction is essential in network routing. Dijkstra algorithm, one of the static routing algorithms, is widely used. When some links develop new weights, dynamic routing algorithms become more efficient than static routing algorithms. This is because dynamic routing algorithms reduce the redundancy caused by re-computing the affected part of the network in regard...

We use a relational characterization of binary direct sums to model sequences within the relation-algebraic manipulation and prototyping system RelView in a simple way. As an application we formally derive a RelView program for computing equivalence classes of an equivalence relation, where we combine relation-algebraic calculations with the so-called Dijkstra-Gries program development method. ...

This paper mainly studies the eradication of the Ebola virus, proposing a scientific system, including three modules for the eradication of Ebola virus. Firstly, we build a basic model combined with nonlinear incidence rate and maximum treatment capacity. Secondly, we use the dynamic programming method and the Dijkstra Algorithm to set up M-S (storage) and several delivery locations in West Afr...

We analyze a simple method for finding shortest paths in Euclidean graphs (where vertices are points in a Euclidean space and edge weights are distances between points). For many graph models, the running time of the algorithm to find the shortest path between a specified pair of vertices in a graph with V vertices and E edges is shown to be O ( V ) as compared with O(V1ogV + E ) required by th...

We show how to verify four challenging concurrent ne-grained graph-manipulating algorithms, including graph copy, a speculativelyparallel Dijkstra and spanning tree. We develop a method of reasoning for such algorithms that dynamically tracks the contributions and responsibilities of each thread operating on a graph, even in cases of arbitrary recursive thread creation. We demonstrate how to us...

This paper provides twenty rules of thumb for comparing algorithms having the same function, one of which is to be selected for use in an intelligent system. The rules are illuminated by a specific example, the comparison of three algorithms for dealing with the collection of open nodes that is at the heart of the Dijkstra graph search method. For each rule, a description is given of how the ru...

We show the testing results of Kruskal, Prim-Dijkstra for finding a low-stretch spanning tree for both unweighted graphs and weighted graphs transformed from benchmark circuits [1]. On unweighted graph, our implementation can get an average stretch of about 7 for all benchmark circuits. Kruskal’s algorithm gives good edge selection for finding short stretch edges, but does not work well for oth...

In proof theory, a standard method for showing the correctness of a program w.r.t. given preand postconditions is to construct a weakest precondition and to show that the precondition implies the weakest precondition. In this paper, graph programs in the sense of Habel and Plump 2001 are extended to programs over high-level rules with application conditions, a formal definition of weakest preco...

In proof theory, a standard method for showing the correctness of a program w.r.t. given preand postconditions is to construct a weakest precondition and to show that the precondition implies the weakest precondition. In this paper, graph programs in the sense of Habel and Plump 2001 are extended to programs over high-level rules with application conditions, a formal definition of weakest preco...