Automation Of Independent Path Searching using Depth First Search

Path-based depth-first search for strong and biconnected components

Depth-first search, as developed by Tarjan and coauthors, is a fundamental technique of efficient algorithm design for graphs [23]. This note presents depth-first search algorithms for two basic problems, strong and biconnected components. Previous algorithms either compute auxiliary quantities based on the depth-first search tree (e.g., LOWPOINT values) or require two passes. We present one-pa...

Interleaved Depth-First Search

In tree search, depth-first search (DFS) often uses ordering successor heuristics. If the heuristic makes a mistake ordering a bad successor (without goals in its subtree) before good ones (wi th goals in their subtrees), DFS has to unsuccessfully traverse the whole bad subtree before f inding a goal. To prevent this useless work, we present a new strategy called interleaved depthfirst search (...

9 Depth-first Search

We can make this algorithm slightly faster (in practice) by checking whether a node is marked before we recursively explore it. This modification ensures that we call DFS(v) only once for each vertex v. We can further modify the algorithm to define parent pointers and other useful information about the vertices. This additional information is computed by two black-box subroutines PREVISIT and P...

Depth First Search

Depth-first search of a graph is formalized with function. It is shown that it visits all of the reachable nodes from a given list of nodes. Executable ML code of depth-first search is obtained with code generation feature of Isabelle/HOL. The formalization contains two implementations of depth-first search: one by stack and one by nested recursion. They are shown to be equivalent. The terminat...

Depth First Search in Graphs