Depth-first search as a combinatorial correspondence

Anytime AND/OR Depth-First Search for Combinatorial Optimization

One popular and efficient scheme for solving combinatorial optimization problems over graphical models exactly is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This article 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AN...

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