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On Treewidth of Social Networks
, M.Sc. Thesis Sharif University of Technology ; Safari, Mohammad Ali (Supervisor) ; Habibi, Jafar (Supervisor)
Abstract
In this thesis, we study the treewidth of social networks. The importance of studding treewidth is for two reasons. The first is that for the graph with bounded treewidth, many optimization problems that are NP-hard in general, can be solved in polynomial or even linear time. The second is that the high value of treewidth in a graph, reflects some high degree of connectivity and robustness, which is an essential factor in designing many networks. But the problem is that determining the value of treewidth in a graph is NP-complete so, computing the treewidth of real complex networks is not feasible. We first review the related works and mention the weakness of the past works, then introduce a...
Releasing All-Pairs Shortest Distances of Public Graphs with Differential Privacy
, M.Sc. Thesis Sharif University of Technology ; Ebrahimi Boroojeni, Javad (Supervisor)
Abstract
In the context of differential privacy, a data holder has confidential information about users. The goal is to provide a randomized algorithm that takes this information as input and outputs an aggregation of the input. The algorithm must have the property that for any neighboring input pairs, the output distribution of the algorithm is close. One problem in differential privacy research is the release of shortest distances in a weighted graph. This model, first studied by Adam Sealfon, involves an edge-weighted graph G=(V, E) with weights w : E → R, where the topology of the graph is public and the private information is the weight of the edges. The aim is to provide an (ϵ, δ)-DP algorithm...
Pure nash equilibria: complete characterization of hard and easy graphical games
, Article Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, 10 May 2010 ; Volume 1 , 2010 , Pages 199-206 ; 15488403 (ISSN) ; 9781617387715 (ISBN) ; Safari, M. A ; Sharif University of Technology
International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
2010
Abstract
We consider the computational complexity of pure Nash equilibria in graphical games. It is known that the problem is NP-complete in general, but tractable (i.e., in P) for special classes of graphs such as those with bounded treewidth. It is then natural to ask: is it possible to characterize all tractable classes of graphs for this problem? In this work, we provide such a characterization for the case of bounded in-degree graphs, thereby resolving the gap between existing hardness and tractability results. In particular, we analyze the complexity of PURE-GG(C, -), the problem of deciding the existence of pure Nash equilibria in graphical games whose underlying graphs are restricted to class...
Efficient approximations for cache-conscious data placement
, Article 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation, PLDI 2022, 13 June 2022 through 17 June 2022 ; 2022 , Pages 857-871 ; 9781450392655 (ISBN) ; Daliri, M ; Goharshady, A.K ; Pavlogiannis, A ; ACM SIGPLAN ; Sharif University of Technology
Association for Computing Machinery
2022
Abstract
There is a huge and growing gap between the speed of accesses to data stored in main memory vs cache. Thus, cache misses account for a significant portion of runtime overhead in virtually every program and minimizing them has been an active research topic for decades. The primary and most classical formal model for this problem is that of Cache-conscious Data Placement (CDP): given a commutative cache with constant capacity k and a sequence ς of accesses to data elements, the goal is to map each data element to a cache line such that the total number of cache misses over ς is minimized. Note that we are considering an offline single-threaded setting in which ς is known a priori. CDP has been...