Results 1 
3 of
3
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
Abstract

Cited by 290 (1 self)
 Add to MetaCart
We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery. 1 Introduction We consider a longstudied generalization of the shortest path problem, in which not one but several short paths must be produced. The k shortest paths problem is to list the k paths connecting a given sourcedestination pair in the digraph with minimum total length. Our techniques also apply to the problem of listing all paths shorter than some given threshhold length. In the version of these problems studi...
kPathA: kshortest Path Algorithm (pronounce as “Qué Pasa”)
"... Abstract—One important aspect of computational systems biology includes the identification and analysis of functional response networks within large biochemical networks. These functional response networks represent the response of a biological system under a particular experimental condition which ..."
Abstract
 Add to MetaCart
Abstract—One important aspect of computational systems biology includes the identification and analysis of functional response networks within large biochemical networks. These functional response networks represent the response of a biological system under a particular experimental condition which can be used to pinpoint critical biological processes. For this purpose, we have developed a novel algorithm to calculate response networks as scored/weighted subgraphs spanned by kshortest simple (loop free) paths. The kshortest simple path algorithm is based on a forward/backward chaining approach synchronized between pairs of processors. The algorithm scales linear with the number of processors used. The algorithm implementation is using a Linux cluster platform, MPI lam and mpiJava messaging as well as the Java language for the application. The algorithm is performed on a hybrid human network consisting of 45,041 nodes and 438,567 interactions together with gene expression information obtained from human celllines infected by influenza virus. Its response networks show the early innate immune response and virus triggered processes within human epithelial cells. Especially under the imminent threat of a pandemic caused by novel influenza strains, such as the current H1N1 strain, these analyses are crucial for a comprehensive understanding of molecular processes during early phases of infection. Such a systems level understanding may aid in the identification of therapeutic markers and in drug development for diagnosis and finally prevention of a potentially dangerous disease. Index Terms—Biological and numerical parallel computing; kshortest path; response network; host response; infectious disease; systems biology, influenza virus I.