Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Graph theoretic heuristics for unequal-sized facility layout problems

Abstract: We consider the unequal-sized facility layout problem with the objective of minimizing total transportation distance. The total transportation distance is defined as the sum of products of flow amounts and rectilinear distances between facilities, where flow amount represents the number of trips per time period between facilities. In the layout problem, it is assumed that shapes of facilities are not fixed and that there is no empty space between facilities in the layout. We propose new graph theoretic heuristics for the problem. In the heuristics, an initial layout is obtained by constructing a planar adjacency graph and then the solution is improved by changing the adjacency graph (not the physical layout). Therefore, these heuristics do not need an initial layout in advance, and sizes and locations of facilities do not have to be considered in the improvement procedure. Computational results showed that the proposed algorithms gave better solutions than those from CRAFT, which is one of the most popular algorithms for unequal-sized facility layout problems.

Multiple Moving Object Detection From UAV Videos Using Trajectories of Matched Regional Adjacency Graphs

Abstract: Image registration has been long used as a basis for the detection of moving objects. Registration techniques attempt to discover correspondences between consecutive frame pairs based on image appearances under rigid and affine transformations. However, spatial information is often ignored, and different motions from multiple moving objects cannot be efficiently modeled. Moreover, image registration is not well suited to handle occlusion that can result in potential object misses. This paper proposes a novel approach to address these problems. First, segmented video frames from unmanned aerial vehicle captured video sequences are represented using region adjacency graphs of visual appearance and geometric properties. Correspondence matching (for visible and occluded regions) is then performed between graph sequences by using multigraph matching. After matching, region labeling is achieved by a proposed graph coloring algorithm which assigns a background or foreground label to the respective region. The intuition of the algorithm is that background scene and foreground moving objects exhibit different motion characteristics in a sequence, and hence, their spatial distances are expected to be varying with time. Experiments conducted on several DARPA VIVID video sequences as well as self-captured videos show that the proposed method is robust to unknown transformations, with significant improvements in overall precision and recall compared to existing works.

String edit distance, random walks and graph matching

Abstract: This paper shows how the eigenstructure of the adjacency matrix can be used for the purposes of robust graph matching. We commence from the observation that the leading eigenvector of a transition probability matrix is the steady state of the associated Markov chain. When the transition matrix is the normalized adjacency matrix of a graph, then the leading eigenvector gives the sequence of nodes of the steady state random walk on the graph. We use this property to convert the nodes in a graph into a string where the node-order is given by the sequence of nodes visited in the random walk. We match graphs represented in this way, by finding the sequence of string edit operations which minimize edit distance.

Maximal Quasi-Bicliques with Balanced Noise Tolerance: Concepts and Co-clustering Applications.

Abstract: The rigid all-versus-all adjacency required by a maximal biclique for its two vertex sets is extremely vulnerable to missing data In the past, several types of quasi-bicliques have been proposed to tackle this problem, however their noise tolerance is usually unbalanced and can be very skewed In this paper, we improve the noise tolerance of maximal quasi-bicliques by allowing every vertex to tolerate up to the same number, or the same percentage, of missing edges This idea leads to a more natural interaction between the two vertex sets— a balanced most-versus-most adjacency This generalization is also non-trivial, as many large-size maximal quasi-biclique subgraphs do not contain any maximal bicliques This observation implies that direct expansion from maximal bicliques may not guarantee a complete enumeration of all maximal quasi-bicliques We present important properties of maximal quasi-bicliques such as a bounded closure property and a fixed point property to design efficient algorithms Maximal quasi-bicliques are closely related to co-clustering problems such as documents and words co-clustering, images and features coclustering, stocks and financial ratios co-clustering, etc Here, we demonstrate the usefulness of our concepts using a new application—a bioinformatics example— where prediction of true protein interactions is investigated