. We conduct an extensive computational study of shortest paths algorithms, including some very recent algorithms. We also suggest new algorithms motivated by the experimental results and prove interesting theoretical results suggested by the experimental data. Our computational study is based

We give a linear-time algorithm for single-source shortest paths in planar graphs with nonnegative edge-lengths. Our algorithm also yields a linear-time algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required

Abstract. We consider standard algorithms of finite graph theory, like for instance shortest path algorithms. We present two general methods to polynomially extend these algorithms to infinite graphs generated by deterministic graph grammars. 1

. A calculational derivation is given of an abstract path algorithm, one instance of the algorithm being Dijkstra's shortest-path algorithm, another being breadth-first/depth-first search of a directed graph. The basis for the derivation is the algebra of regular languages. 1 Problem

In this paper, we report on our own experience in studying a fundamental problem on graphs: all pairs shortest paths. In particular, we discuss the interplay between theory and practice in engineering a simple variant of Dijkstra's shortest path algorithm. In this context, we show

Dijkstra’s algorithm solves the single-source shortest path problem on any directed graph in O(m + n log n) worst-case time when a Fibonacci heap is used as the frontier set data structure. Here n is the number of vertices and m is the number of edges in the graph. If the graph is nearly acyclic

elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

to explain the striking algorithmic component of Milgram’s original findings: that individuals using local information are collectively very effective at actually constructing short paths between two points in a social network. Although recently proposed network models are rich in short paths, we prove

required by earlier algorithms. First, the paper states the maximum flow problem, gives the Ford-Fulkerson labeling method for its solution, and points out that an improper choice of flow augmenting paths can lead to severe computational difficulties. Then rules of choice that avoid these difficulties

Shortest paths, or close to shortest paths, are commonly used in everyday situations. The paper reviews the various algorithms available for the problem. One of the famous technique Dijkstra’s algorithm solves the single-source shortest path problem on any directed graph in O(m+nlogn) worst