3-connected Planar Graph Isomorphism is in Log-space
نویسندگان
چکیده
We consider the isomorphism and canonization problem for 3-connected planar graphs. The problem was known to be L -hard and in UL ∩ coUL [TW08]. In this paper, we give a deterministic log-space algorithm for 3-connected planar graph isomorphism and canonization. This gives an L -completeness result, thereby settling its complexity. The algorithm uses the notion of universal exploration sequences from [Kou02] and [Rei05]. To our knowledge, this is a completely new approach to graph canonization.
منابع مشابه
Graph Isomorphism for K_{3, 3}-free and K_5-free graphs is in Log-space
Graph isomorphism is an important and widely studied computational problem with a yet unsettled complexity. However, the exact complexity is known for isomorphism of various classes of graphs. Recently, [8] proved that planar isomorphism is complete for log-space. We extend this result further to the classes of graphs which exclude K3,3 or K5 as a minor, and give a log-space algorithm. Our algo...
متن کاملParameterized Graph Cleaning Problems
We investigate the Induced Subgraph Isomorphism problem with non-standard parametrization, where the parameter is the difference |V (G)| − |V (H)| with H and G being the smaller and the larger input graph, respectively. Intuitively, we can interpret this problem as “cleaning” the graph G, regarded as a pattern containing extra vertices indicating errors, in order to obtain the graph H represent...
متن کاملDynamic Complexity of Planar 3-Connected Graph Isomorphism
Dynamic Complexity (as introduced by Patnaik and Immerman [13]) tries to express how hard it is to update the solution to a problem when the input is changed slightly. It considers the changes required to some stored data structure (possibly a massive database) as small quantities of data (or a tuple) are inserted or deleted from the database (or a structure over some vocabulary). The main diff...
متن کاملSubexponential Time Algorithms for Embedding H-Minor Free Graphs
We establish the complexity of several graph embedding problems: Subgraph Isomorphism, Graph Minor, Induced Subgraph and Induced Minor, when restricted to H-minor free graphs. In each of these problems, we are given a pattern graph P and a host graph G, and want to determine whether P is a subgraph (minor, induced subgraph or induced minor) of G. We show that, for any fixed graph H and > 0, if ...
متن کاملParallel Tree Contraction, Part 2: Further Applications
This paper applies the parallel tree contraction techniques developed in Miller and Reif's paper [Randomness and Computation, Vol. 5, S. Micali, ed., JAI Press, 1989, pp. 47-72] to a number of fundamental graph problems. The paper presents an O(1ogn) time and nl logn processor, a 0-sided randomized algorithm for testing the isomorphism of trees, and an O(log n) time, n-processor algorithm for m...
متن کامل