Matchings and Pfaffians Matchings and Pfaffians      

By  Kannan Nambiar, Former Dean and Professor, JNU, India , On March 7, 2011

Pfaffian of a skew symmetric matrix obtained from an undirected graph is used to enumerate the macthings in the graph.

A O(|E|) Time Shortest Path Algorithm For Non- Negative Weighted Undirected Graphs A O(|E|) Time Shortest Path Algorithm For Non- Negative Weighted Undirected Graphs      

By  Ijcsis Editor, On November 10, 2009

In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points—source and destination, and it is not necessary to calculate the shortest path from source to all other nodes. This paper concentrates on this very idea and presents an algorithm for calculating shortest path for (i) nonnegative weighted undirected graphs (ii) unweighted undirected graphs. The algorithm completes its execution in O(|E|) for all graphs except few in which longer path (in terms of number of edges) from source to some node makes it best selection for that node. The main advantage of the algorithms is its simplicity and it does not need complex data structures for implementations.