k-PathA: k-shortest Path Algorithm

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 sub-graphs spanned by k-shortest simple (loop free) paths. The k-shortest 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 cell-lines 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

An adaptive distributed Dijkstra shortest path algorithm

Cover title.Includes bibliographical references.Supported in part by the Codex Corporation. Supported in part by the Army Research Office. DAAL03-86-K-0171Pierre A. Humblet

Calculating path algorithms

AbstractA calculational derivation is given of two abstract path algorithms. The first is an all-pairs algorithm, two well-known instances of which are Warshall's (reachability) algorithm and Floyd's shortest-path algorithm; instances of the second are Dijkstra's shortest-path algorithm and breadth-first/depth-first search of a directed graph. The basis for the derivations is the algebra of regular languages

Smoothed Analysis of the Successive Shortest Path Algorithm

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that both the problem and the algorithms are well understood. However, some of the algorithms' running times observed in empirical studies contrast the running times obtained by worst-case analysis not only in the order of magnitude but also in the ranking when compared to each other. For example, the Successive Shortest Path (SSP) algorithm, which has an exponential worst-case running time, seems to outperform the strongly polynomial Minimum-Mean Cycle Canceling algorithm. To explain this discrepancy, we study the SSP algorithm in the framework of smoothed analysis and establish a bound of $O(mn\phi)$ for the number of iterations, which implies a smoothed running time of $O(mn\phi (m + n\log n))$, where $n$ and $m$ denote the number of nodes and edges, respectively, and $\phi$ is a measure for the amount of random noise. This shows that worst-case instances for the SSP algorithm are not robust and unlikely to be encountered in practice. Furthermore, we prove a smoothed lower bound of $\Omega(m \phi \min\{n, \phi\})$ for the number of iterations of the SSP algorithm, showing that the upper bound cannot be improved for $\phi = \Omega(n)$.Comment: A preliminary version has been presented at SODA 201