2026-08-17T17:45:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24546 2025-12-16T14:00:39Z ddc:004 open_access

Testing Depth First Search Numbering Czumaj, Artur Sohler, Christian Walzer, Stefan Randomized Algorithms Graph Algorithms Property Testing Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with sublinear query complexity. Here, a graph property P is testable with a sublinear query complexity if there is an algorithm that makes a sublinear number of queries to the input graph and accepts with probability at least 2/3, if the graph has property P, and rejects with probability at least 2/3 if it is ε-far from every graph that has property P. In this paper, we introduce a new variant of the bounded degree graph model. In this variant, in addition to the standard representation of a bounded degree graph, we assume that every vertex v has a unique label num(v) from {1, … , |V|}, and in addition to the standard queries in the bounded degree graph model, we also allow a property testing algorithm to query for the label of a vertex (but not for a vertex with a given label). Our new model is motivated by certain graph processes such as a DFS traversal, which assign consecutive numbers (labels) to the vertices of the graph. We want to study which of these numberings can be tested in sublinear time. As a first step in understanding such a model, we develop a property testing algorithm for discovery times of a DFS traversal with query complexity O(n^{1/3}/ε) and for constant ε > 0 we give a matching lower bound. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Artur Czumaj and Christian Sohler and Stefan Walzer 2025 Is Part Of LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2025.78 urn:nbn:de:0030-drops-245466 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.78 eng https://creativecommons.org/licenses/by/4.0/legalcode