Simple Examples of Sublinear-time Algorithms for Graphs 1.1 Definitions
نویسندگان
چکیده
For sublinear-time algorithms, it is crucial how input is represented and accessed. Depending on input representation and queries allowed, we might or might not be able to solve a given problem in sublinear time. In addition, in the property testing model, the correctness guarantee of the algorithm depends on the distance between objects, which is typically normalized by the size of the input. The set of inputs that a test is required to reject (the ones that are -far) depends on the size of the representation. There are two models for graph representation, one appropriate for working with sparse graphs and the other – with dense graphs.
منابع مشابه
STCON in Directed Unique-Path Graphs
We study the problem of space-efficient polynomial-time algorithms for directed stconnectivity (STCON). Given a directed graph G, and a pair of vertices s, t, the STCON problem is to decide if there exists a path from s to t in G. For general graphs, the best polynomial-time algorithm for STCON uses space that is only slightly sublinear. However, for special classes of directed graphs, polynomi...
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملSeminar on Sublinear Time Algorithms: Testing Bipartiteness in Bounded Degree Graphs
Overview • Testing bipartiteness in sparse graphs • In dense graphs: Upperbound of poly(1) [1] – Sample vertices at random and test if their induced subgraph is bi-partite [No proof] • In sparse graphs we will see: – Upperbound of O(√ n · poly((lg n)//) [2] * We will analyze only the simple case of rapidly mixing graphs * Algorithm works much the say way for general graphs
متن کاملSublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs
For a graph G, let Z(G, λ) be the partition function of the monomer-dimer system defined by ∑ k mk(G)λ , where mk(G) is the number of matchings of size k in G. We consider graphs of bounded degree and develop a sublinear-time algorithm for estimating logZ(G, λ) at an arbitrary value λ > 0 within additive error ǫn with high probability. The query complexity of our algorithm does not depend on th...
متن کاملSublinear graph augmentation for fast query implementation
We introduce the problem of augmenting graphs with sublinear memory in order to speed up replies to queries. As a concrete example, we focus on the following problem: the input is an (unpartitioned) bipartite graph G = (V,E). Given a query v ∈ V , the algorithm’s goal is to output v’s color in some legal 2-coloring of G, using few probes to the graph. All replies have to be consistent with the ...
متن کامل