Topic
Windmill graph
About: Windmill graph is a research topic. Over the lifetime, 1349 publications have been published within this topic receiving 27973 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: Two backtracking algorithms are presented, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique, and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed.
Abstract: Description bttroductian. A maximal complete subgraph (clique) is a complete subgraph that is not contained in any other complete subgraph. A recent paper [1] describes a number of techniques to find maximal complete subgraphs of a given undirected graph. In this paper, we present two backtracking algorithms, using a branchand-bound technique [4] to cut off branches that cannot lead to a clique. The first version is a straightforward implementation of the basic algorithm. It is mainly presented to illustrate the method used. This version generates cliques in alphabetic (lexicographic) order. The second version is derived from the first and generates cliques in a rather unpredictable order in an attempt to minimize the number of branches to be traversed. This version tends to produce the larger cliques first and to generate sequentially cliques having a large common intersection. The detailed algorithm for version 2 is presented here. Description o f the algorithm--Version 1. Three sets play an important role in the algorithm. (1) The set compsub is the set to be extended by a new point or shrunk by one point on traveling along a branch of the backtracking tree. The points that are eligible to extend compsub, i.e. that are connected to all points in compsub, are collected recursively in the remaining two sets. (2) The set candidates is the set of all points that will in due time serve as an extension to the present configuration of compsub. (3) The set not is the set of all points that have at an earlier stage already served as an extension of the present configuration of compsub and are now explicitly excluded. The reason for maintaining this set trot will soon be made clear. The core of the algorithm consists of a recursively defined extension operator that will be applied to the three sets Just described. It has the duty to generate all extensions of the given configuration of compsub that it can make with the given set of candidates and that do not contain any of the points in not. To put it differently: all extensions of compsub containing any point in not have already been generated. The basic mechanism now consists of the following five steps:
2,696 citations
TL;DR: In this article, the generalized vertex median of a weighted graph may be found by complete enumeration or by some heuristic method, and a method that seems to perform well in comparison with others found in the literature is proposed.
Abstract: The generalized vertex median of a weighted graph may be found by complete enumeration or by some heuristic method. This paper investigates alternatives and proposes a method that seems to perform well in comparison with others found in the literature.
870 citations
TL;DR: In this article, the authors present a survey of the relations among the circular chromatic number, the chromatic numbers and some other parameters of a graph, and pose 28 open problems and discuss partial results and references for each of these problems.
425 citations
14 Jun 2009
TL;DR: Experimental results on both artificial data and real benchmark datasets indicate that b-matching produces more robust graphs and therefore provides significantly better prediction accuracy without any significant change in computation time.
Abstract: Graph based semi-supervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method and its effect on performance. This article provides an empirical study of leading semi-supervised methods under a wide range of graph construction algorithms. These SSL inference algorithms include the Local and Global Consistency (LGC) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular k-nearest neighbors method (kNN) and the b-matching method. As opposed to the greedily constructed kNN graph, the b-matched graph ensures each node in the graph has the same number of edges and produces a balanced or regular graph. Experimental results on both artificial data and real benchmark datasets indicate that b-matching produces more robust graphs and therefore provides significantly better prediction accuracy without any significant change in computation time.
418 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 6 |
| 2023 | 14 |
| 2022 | 30 |
| 2021 | 4 |
| 2020 | 4 |