Graphs where Search Methods are Indistinguishable
Matja\v{z} Krnc, Nevena Piva\v{c}

TL;DR
This paper characterizes classes of graphs where different search algorithms produce identical vertex orderings, enhancing understanding of their relationships and aiding algorithm design.
Contribution
It provides a comprehensive characterization of graph families where ten pairs of common search methods yield indistinguishable vertex orderings.
Findings
Characterization of graph families for BFS and DFS
Characterization of graph families for LexBFS and LexDFS
Characterization of graph families for MNS and other searches
Abstract
Graph searching is one of the simplest and most widely used tools in graph algorithms. Every graph search method is defined using some particular selection rule, and the analysis of the corresponding vertex orderings can aid greatly in devising algorithms, writing proofs of correctness, or recognition of various graph families. We study graphs where the sets of vertex orderings produced by two different search methods coincide. We characterise such graph families for ten pairs from the best-known set of graph searches: Breadth First Search (BFS), Depth First Search (DFS), Lexicographic Breadth First Search (LexBFS) and Lexicographic Depth First Search (LexDFS), and Maximal Neighborhood Search (MNS).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Theory and Algorithms · Constraint Satisfaction and Optimization
