Adjacency list

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

Graph Homomorphisms for Quantum Players

Abstract: A homomorphism from a graph X to a graph Y is an adjacency preserving mapping f:V(X) -> V(Y). We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y. This is a generalization of the well-studied graph coloring game. Via systematic study of quantum homomorphisms we prove new results for graph coloring. Most importantly, we show that the Lovasz theta number of the complement lower bounds the quantum chromatic number, which itself is not known to be computable. We also show that other quantum graph parameters, such as quantum independence number, can differ from their classical counterparts. Finally, we show that quantum homomorphisms closely relate to zero-error channel capacity. In particular, we use quantum homomorphisms to construct graphs for which entanglement-assistance increases their one-shot zero-error capacity.

Central Limit Theorem for the Adjacency Operators on the Infinite Symmetric Group

Abstract: An adjacency operator on a group is a formal sum of (left) regular representations over a conjugacy class. For such adjacency operators on the infinite symmetric group which are parametrized by the Young diagrams, we discuss the correlation of their powers with respect to the vacuum vector state. We compute exactly the correlation function under suitable normalization and through the infinite volume limit. This approach is viewed as a central limit theorem in quantum probability, where the operators are interpreted as random variables via spectral decomposition. In [K], Kerov showed the corresponding result for one-row Young diagrams. Our formula provides an extension of Kerov's theorem to the case of arbitrary Young diagrams.

Large-Scale Aerial Image Categorization Using a Multitask Topological Codebook

Abstract: Fast and accurately categorizing the millions of aerial images on Google Maps is a useful technique in pattern recognition. Existing methods cannot handle this task successfully due to two reasons: 1) the aerial images’ topologies are the key feature to distinguish their categories, but they cannot be effectively encoded by a conventional visual codebook and 2) it is challenging to build a realtime image categorization system, as some geo-aware Apps update over 20 aerial images per second. To solve these problems, we propose an efficient aerial image categorization algorithm. It focuses on learning a discriminative topological codebook of aerial images under a multitask learning framework. The pipeline can be summarized as follows. We first construct a region adjacency graph (RAG) that describes the topology of each aerial image. Naturally, aerial image categorization can be formulated as RAG-to-RAG matching. According to graph theory, RAG-to-RAG matching is conducted by enumeratively comparing all their respective graphlets (i.e., small subgraphs). To alleviate the high time consumption, we propose to learn a codebook containing topologies jointly discriminative to multiple categories. The learned topological codebook guides the extraction of the discriminative graphlets. Finally, these graphlets are integrated into an AdaBoost model for predicting aerial image categories. Experimental results show that our approach is competitive to several existing recognition models. Furthermore, over 24 aerial images are processed per second, demonstrating that our approach is ready for real-world applications.

Privacy-Preserving Approach PBCN in Social Network With Differential Privacy

Abstract: Currently, lots of real social relations in social networks force users to face the potential risk of privacy leakage. Consequently, data holders would like to disturbor anonymize their individual data before publishing them, for the purpose of privacy protection. Due to the characteristics of high sensitivity and large volume data of social network graph structure, it is difficult for privacy protection schemes to enable a reasonable allocation of noises while keeping desirable data availability and execution efficiency. On the basis of differential privacy model, combining with clustering and randomization algorithms, a privacy protection approach PBCN (Privacy Preserving Approach Based on Clustering and Noise) is proposed. This proposal is composed of five algorithms including random disturbance based on clustering, graph reconstruction after disturbing degree sequence and noise nodes generation, etc. Furthermore, a privacy measure algorithm based on adjacency degree is put forward in order to objectively evaluate the privacy-preserving strength of various schemes against graph structure and degree attacks. Simulation experiments are conducted to achieve performance comparisons between PBCN, Spctr Add/Del, Spctr Switch, DER and HPDP. The experimental results show that PBCN realizes more satisfactory data availability and execution efficiency. Finally, parameters utility analysis demonstrates PBCN can achieve a “trade-off” between data availability and privacy protection level.