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On decomposing complete tripartite graphs into 5-cycles
, Article Australasian Journal of Combinatorics ; Volume 54, Issue 2 , 2012 , Pages 289-301 ; 10344942 (ISSN) ; Mahmoodian, E. S ; Mollaahmadi, E ; Sharif University of Technology
AJC
2012
Abstract
The problem of finding necessary and sufficient conditions to decompose a complete tripartite graph K(r, s, t) into 5-cycles was first considered by Mahmoodian and Mirzakhani (1995). They stated some necessary conditions and conjectured that these conditions are also sufficient. Since then, many cases of the problem have been solved by various authors; however the case when the partite sets r ≤ s ≤ t have odd and distinct sizes remains open. A necessary condition is t ≤ 3r. Billington and Cavenagh (2011) have shown that when r, s, and t are all odd and r ≤ s ≤ t ≤ κr, where κ ≈ 1.0806, then the conjectured necessary conditions for decomposing are also sufficient. We extend this result...
On the complexity of isoperimetric problems on trees [electronic resource]
, Article Discrete Applied Mathematics ; Volume 160 Issue 1-2, January, 2012 Pages 116-131 ; Javadi, Ramin ; Sharif Univercity of Technology
Abstract
This paper is aimed at investigating some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimetric numbers defined through taking the minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a partition/subpartition. We show that the decision problem for the case of taking k-partitions and the maximum (called the max normalized cut problem NCP^M), and the other two decision problems for the mean version (referred to as IPP^m and NCP^m) are NP-complete problems for weighted trees. On...
Spectral Graph Partitioning
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
Graph partitioning, or graph clustering, is an essential researa problem in many areas. In this thesis, we focus on the partitioning problem of unweighted undirected graph, that is, graphs for which the weight of all edges is 1. We will investigate spectral methods for solving the graph partitioning and we compare them. In addition to theoretical analysis,We also implement some of spectral algorithms in matlab and apply them on standard graph data sets. Finally, the experimental
results obtained are offering
results obtained are offering
A graph-theoretic approach toward autonomous skill acquisition in reinforcement learning
, Article Evolving Systems ; Volume 9, Issue 3 , 2018 , Pages 227-244 ; 18686478 (ISSN) ; Taghizadeh, N ; Beigy, H ; Sharif University of Technology
Springer Verlag
2018
Abstract
Hierarchical reinforcement learning facilitates learning in large and complex domains by exploiting subtasks and creating hierarchical structures using these subtasks. Subtasks are usually defined through finding subgoals of the problem. Providing mechanisms for autonomous subgoal discovery and skill acquisition is a challenging issue in reinforcement learning. Among the proposed algorithms, a few of them are successful both in performance and also efficiency in terms of the running time of the algorithm. In this paper, we study four methods for subgoal discovery which are based on graph partitioning. The idea behind the methods proposed in this paper is that if we partition the transition...
Clustering and outlier detection using isoperimetric number of trees
, Article Pattern Recognition ; Volume 46, Issue 12 , December , 2013 , Pages 3371-3382 ; 00313203 (ISSN) ; Javadi, R ; Shariat Razavi, S. B ; Sharif University of Technology
2013
Abstract
We propose a graph-based data clustering algorithm which is based on exact clustering of a minimum spanning tree in terms of a minimum isoperimetry criteria. We show that our basic clustering algorithm runs in O(nlogn) and with post-processing in almost O(nlogn) (average case) and O(n2) (worst case) time where n is the size of the data-set. It is also shown that our generalized graph model, which also allows the use of potentials at vertices, can be used to extract an extra piece of information related to anomalous data patterns and outliers. In this regard, we propose an algorithm that extracts outliers in parallel to data clustering. We also provide a comparative performance analysis of...
On the complexity of isoperimetric problems on trees
, Article Discrete Applied Mathematics ; Volume 160, Issue 1-2 , January , 2012 , Pages 116-131 ; 0166218X (ISSN) ; Javadi, R ; Sharif University of Technology
2012
Abstract
This paper is aimed at investigating some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called minimum normalized cuts/isoperimetric numbers defined through taking the minimum of the maximum or the mean of the normalized outgoing flows from a set of subdomains of vertices, where these subdomains constitute a partition/subpartition. We show that the decision problem for the case of taking k-partitions and the maximum (called the max normalized cut problem NCPM), and the other two decision problems for the mean version (referred to as IPPm and NCPm) are NP-complete problems for weighted trees. On the...
Graph-based Decomposition of Multi Input Nonlinear Dynamical Systems
, M.Sc. Thesis Sharif University of Technology ; Haeri, Mohammad (Supervisor)
Abstract
In this thesis, partitioning of multi inputs nonlinear dynamical systems into distinct subsystems with the goal of designing decentralized, distributed, and cooperative predictive controllers for reducing the computational load and time in practical implementations has been studied. At first, the concept of dynamical systems graph is introduced and the problem of decomposing nonlinear dynamical systems into distinct subsystems has been converted to the problem of decomposing dynamical systems graph into separate subgraphs. The proposed method for decomposition of the dynamical system graph is represented as a linear integer optimization programing where the separated subgraphs is obtained by...
On Graph Partitioning Algorithms And It’s Applications in Image Segmentation
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
The problem of partitioning vertices of a graph has been studied with different formulations according to their application. In this thesis we try to review some of these formulations and existing algorithms. In addition we try to investigate the correct definition for a specific application in image processing, namely image segmentation. At the end, we propose a new algorithm for partitioning vertices of a weighted graph according to the mentioned application and compare its performance with some similar algorithms
A Comprehensive Method for Clustering Evolutionary Big Graphs
, M.Sc. Thesis Sharif University of Technology ; Khedmati, Majid (Supervisor)
Abstract
Today, many real-world datasets such as social network data and web pages can be shown as graphs. Community detection and clustering of these big graphs has many applications in different fields like recommender systems in social networks and Diag- nosis of diseases in communication networks among proteins. A cluster in a graph is a sub-graph with many internal and few external edges. A new method for local cluster detection around an existing vertex is introduced in this paper. This method applies random walk algorithm for cluster detection. The time complexity of this algorithm based on the graph size is polynomial. Therefore, it can be used for clustering of big graphs. The experimental...
Graph orientation with splits
, Article 5th International Symposium on Combinatorial Optimization, ISCO 2018, 11 April 2018 through 13 April 2018 ; Volume 10856 LNCS , 2018 , Pages 52-63 ; 03029743 (ISSN); 9783319961507 (ISBN) ; Jansson, J ; Miyano, E ; Nikpey, H ; Ono, H ; Sharif University of Technology
Springer Verlag
2018
Abstract
The Minimum Maximum Outdegree Problem (MMO) is to assign a direction to every edge in an input undirected, edge-weighted graph so that the maximum weighted outdegree taken over all vertices becomes as small as possible. In this paper, we introduce a new variant of MMO called the p-Split Minimum Maximum Outdegree Problem (p-Split-MMO) in which one is allowed to perform a sequence of p split operations on the vertices before orienting the edges, for some specified non-negative integer p, and study its computational complexity. © 2018, Springer International Publishing AG, part of Springer Nature
Automatic discovery of subgoals in reinforcement learning using strongly connected components
, Article 15th International Conference on Neuro-Information Processing, ICONIP 2008, Auckland, 25 November 2008 through 28 November 2008 ; Volume 5506 LNCS, Issue PART 1 , 2009 , Pages 829-834 ; 03029743 (ISSN); 3642024890 (ISBN); 9783642024894 (ISBN) ; Beigy, H ; Asia Pacific Neural Network Assembly (APNNA); International Neural Network Society (INNS); IEEE Computational Intelligence Society; Japanese Neural Network Society (JNNS); European Neural Network Society (ENNS) ; Sharif University of Technology
2009
Abstract
The hierarchical structure of real-world problems has resulted in a focus on hierarchical frameworks in the reinforcement learning paradigm. Preparing mechanisms for automatic discovery of macro-actions has mainly concentrated on subgoal discovery methods. Among the proposed algorithms, those based on graph partitioning have achieved precise results. However, few methods have been shown to be successful both in performance and also efficiency in terms of time complexity of the algorithm. In this paper, we present a SCC-based subgoal discovery algorithm; a graph theoretic approach for automatic detection of subgoals in linear time. Meanwhile a parameter tuning method is proposed to find the...
Mean isoperimetry with control on outliers: Exact and approximation algorithms
, Article Theoretical Computer Science ; Volume 923 , 2022 , Pages 348-365 ; 03043975 (ISSN) ; Daneshgar, A ; Foroughmand-Araabi, M. H ; Sharif University of Technology
Elsevier B.V
2022
Abstract
Given a weighted graph G=(V,E) with weight functions c:E→R+ and π:V→R+, and a subset U⊆V, the normalized cut value for U is defined as the sum of the weights of edges exiting U divided by the weight of vertices in U. The mean isoperimetry problem, ISO1(G,k), for a weighted graph G is a generalization of the classical uniform sparsest cut problem in which, given a parameter k, the objective is to find k disjoint nonempty subsets of V minimizing the average normalized cut value of the parts. The robust version of the problem seeks an optimizer where the number of vertices that fall out of the subpartition is bounded by some given integer 0≤ρ≤|V|. The problem may also be considered as the...
Exact and Approximation Algorithms for the Isoperimetry Problem
, Ph.D. Dissertation Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
Graph partitioning and clustering are among the most important problems in computer science and engineering with a wide range of applications, to which a large number of research projects have attended. The normalized cut ratio is one of the best metrics for graph partitioning, giving rise to the ``Isoperimetry'' problem, which is, however, a challenging problem in its various forms. In this dissertation, we investigate the Isoperimetry problem. %, focusing on the Mean version. We prove that the Mean Isoperimetry problem on edge-weighted trees is solvable in strongly polynomial time. The algorithm can accomodate a wide range of constraints on the problem in the connected regime, including...
A distributed task migration scheme for mesh-based chip-multiprocessors
, Article Parallel and Distributed Computing, Applications and Technologies, PDCAT Proceedings, 20 October 2011 through 22 October 2011 ; Oct , 2011 , Pages 24-29 ; 9780769545646 (ISBN) ; Modarresi, M ; Sarbazi Azad, H ; Sharif University of Technology
Abstract
A task migration scheme for homogeneous chip multiprocessors (CMP) is presented in this paper. The proposed migration mechanism focuses on the communication sub-system and aims to reduce the total power consumption and latency of the network-on-chip (NoC). In this work, starting from an initial mapping, the tasks migrate to new cores in such a way that the distance between the end-point nodes of high-volume communication flows is reduced. Finding the new place for a task is done in a distributed manner by applying an iterative local search that relies on the local information of each task about its communication demand. The task migration procedure also includes a pre-migration step that...
Fast temporal path localization on graphs via multiscale viterbi decoding
, Article IEEE Transactions on Signal Processing ; Volume 66, Issue 21 , 2018 , Pages 5588-5603 ; 1053587X (ISSN) ; Chen, S ; Maddah Ali, M. A ; Grover, P ; Kar, S ; Kovacevic, J ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
We consider a problem of localizing a temporal path signal that evolves over time on a graph. A path signal represents the trajectory of a moving agent on a graph in a series of consecutive time stamps. Through combining dynamic programing and graph partitioning, we propose a path-localization algorithm with significantly reduced computational complexity. To analyze the localization performance, we use two evaluation metrics to quantify the localization error: The Hamming distance and the destination's distance between the ground-truth path and the estimated path. In random geometric graphs, we provide a closed-form expression for the localization error bound, and a tradeoff between...