A simple linear expected time algorithm for finding a hamilton path

A Practical Shortest Path Algorithm with Linear Expected Time

A Simple Linear-Time Algorithm for Finding Path-Decompositions of Small Width

We described a simple algorithm running in linear time for each fixed constant, k, that either establishes that the pathwidth of a graph G is greater than k, or finds a path-decomposition of G of width at most O(zk). This provides a simple proof of the result by Bodlaender that many families of graphs of bounded pathwidth can be recognized in linear time.

Linear Expected Time of a Simple Union-Find Algorithm

This paper presents an analysis of a simple tree-structured disjoint set Union-Find algorithm, and shows that this algorithm requires between n and 2n steps on the average to execute a sequence of n Union and Find instructions, assuming that each pair of existing classes is equally likely to be merged by a Union instruction. Union-Find algorithms are useful in the solution to a number of proble...

A Simple Shortest Path Algorithm with Linear Average Time

We present a simple shortest path algorithm. If the input lengths are positive and uniformly distributed, the algorithm runs in linear time. The worst-case running time of the algorithm is O(m + n logC), where n and m are the number of vertices and arcs of the input graph, respectively, and C is the ratio of the largest and the smallest nonzero arc length.

A Polynomial Time Algorithm for Hamilton Cycle (Path)

This research develops a polynomial time algorithm for Hamilton Cycle(Path) and proves its correctness. A program is developed according to this algorithm and it works very well. This paper declares the research process, algorithm as well as its proof, and the experiment data. Even only the experiment data is a breakthrough.