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graph-representation
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Deep Networks for Graph Classification
, M.Sc. Thesis Sharif University of Technology ; Soleymani Baghshah, Mahdieh (Supervisor)
Abstract
Graphs are widely used for representing structured data and analysis of them is an important area that appears in a broad domain of applications. Graph processing is of great importance in analyzing and predicting social media users' behavior, examining financial markets, detecting malware programs, and designing recombinant drugs. For example, consider a graph in which nodes and edges show the financial institutions and the financial connection between these institutions, respectively. Financial connection refers to the investment of one institute by another. Based on the graph structure, predicting trade stability and balance is extremely significant in macro decisions.In the last few...
On the Computational Complexity of Graph Problems
, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor)
Abstract
Computational complexity of graph problems is an important branch in the-oretical computer science. We introduce to some of ideas for computing the complexity of graph problems with some kind and beautiful examples. Next, we show hardness and inapproximability of some problems. Representation number of graphs has been introduce by Pavel Erdos by Number theory. We prove n1−ϵ inapproximability of that. Lucky number η has been studied by Grytczuk et.al . We show for planar and 3-colorable graphs, it is NP-Complete whether η = 2. Note that since a conjecture, for those graphs, 2 ≤ η ≤ 3. Also for each k ≥ 2, we show NP-completeness of η ≤ k for the graphs. Proper orientation number −→ is a...
Graph Generation by Deep Generative Models
, M.Sc. Thesis Sharif University of Technology ; Khedmati, Majid (Supervisor)
Abstract
Graphs are a language to describe and analyze connections and relations. Recent developments have increased graphs' applications in real-world problems such as social networks, researchers' collaborations, and chemical compounds. Now that we can extract graphs from real life, how can we model and generate graphs similar to a set of known graphs or that are very likely to exist but haven't been discovered yet? Therefore, this research will focus on the problem of graph generation. In graph generation, a set of graphs is a training dataset, and the goal of the thesis is to present an improved deep generative model to learn the training data's distribution, structure, and features.Identifying...
Recommender Systems Based on Knowledge Graphs
, M.Sc. Thesis Sharif University of Technology ; Beigy, Hamid (Supervisor)
Abstract
The widespread use of internet systems and their popularity have led to an increase in the need for recommender systems, and extensive research has been done to address this need. Systems that suggest desirable options to users based on available information are recognized as recommender systems. Important examples of these systems exist in online stores and social networks. In online shops, data specific to each user is very limited and there are limited connections between users and products, which poses challenges for recommender systems. Incomplete or incorrect data may also cause errors in the system, such that the system performs the recommendation process based on wrong information....
Graph-based altruistic games for interference mitigation in femtocell networks
, Article 26th IEEE Annual International Symposium on Personal, Indoor, and Mobile Radio Communications, PIMRC 2015, 30 August 2015 through 2 September 2015 ; Volume 2015-December , 2015 , Pages 1883-1888 ; 9781467367820 (ISBN) ; Khalaj, B. H ; Sharif University of Technology
Abstract
Femtocell networks are a common means of offloading in current mobile networks. Game theoretic and learning-based self-organization schemes are known as two viable approaches for interference control in co-existing macro/femtocell networks. Nevertheless, extensions of these schemes to concurrent multi-agent scenarios often face several challenges including high computational complexity, cyclic behaviors, and lack of convergence. This paper addresses such challenges by introducing local games based on a graph representation of the network. The goal of the games is to optimize the aggregate network capacity through power control. Fairness among femtocells and quality of service (QoS) for...
Algorithmic complexity of weakly semiregular partitioning and the representation number
, Article Theoretical Computer Science ; 2017 ; 03043975 (ISSN) ; Dehghan, A ; Mollahajiaghaei, M ; Sharif University of Technology
Elsevier B.V
2017
Abstract
A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2 δ(T)+O(1), where δ(T) denotes the maximum...
Algorithmic complexity of weakly semiregular partitioning and the representation number
, Article Theoretical Computer Science ; Volume 674 , 2017 , Pages 60-72 ; 03043975 (ISSN) ; Dehghan, A ; Mollahajiaghaei, M ; Sharif University of Technology
Elsevier B.V
2017
Abstract
A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2Δ(T)+O(1), where Δ(T) denotes the maximum...
Deep graph generators: A survey
, Article IEEE Access ; Volume 9 , 2021 , Pages 106675-106702 ; 21693536 (ISSN) ; Ommi, Y ; Soleymani Baghshah, M ; Rabiee, H. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2021
Abstract
Deep generative models have achieved great success in areas such as image, speech, and natural language processing in the past few years. Thanks to the advances in graph-based deep learning, and in particular graph representation learning, deep graph generation methods have recently emerged with new applications ranging from discovering novel molecular structures to modeling social networks. This paper conducts a comprehensive survey on deep learning-based graph generation approaches and classifies them into five broad categories, namely, autoregressive, autoencoder-based, reinforcement learning-based, adversarial, and flow-based graph generators, providing the readers a detailed description...