On the Parameterized Complexity of Sparsest Cut and Small-set Expansion Problems

We study the NP-hard \textsc{$k$-Sparsest Cut} problem ($k$SC) in which, given an undirected graph $G = (V, E)$ and a parameter $k$, the objective is to partition vertex set into $k$ subsets whose maximum edge expansion is minimized. Herein, the edge expansion of a subset $S \subseteq V$ is defined as the sum of the weights of edges exiting $S$ divided by the number of vertices in $S$. Another problem that has been investigated is \textsc{$k$-Small-Set Expansion} problem ($k$SSE), which aims to find a subset with minimum edge expansion with a restriction on the size of the subset. We extend previous studies on $k$SC and $k$SSE by inspecting their parameterized complexity. On the positive side, we present two FPT algorithms for both $k$SSE and 2SC problems where in the first algorithm we consider the parameter treewidth of the input graph and uses exponential space, and in the second we consider the parameter vertex cover number of the input graph and uses polynomial space. Moreover, we consider the unweighted version of the $k$SC problem where $k \geq 2$ is fixed and proposed two FPT algorithms with parameters treewidth and vertex cover number of the input graph. We also propose a randomized FPT algorithm for $k$SSE when parameterized by $k$ and the maximum degree of the input graph combined. Its derandomization is done efficiently. \noindent On the negative side, first we prove that for every fixed integer $k,\tau\geq 3$, the problem $k$SC is NP-hard for graphs with vertex cover number at most $\tau$. We also show that $k$SC is W[1]-hard when parameterized by the treewidth of the input graph and the number~$k$ of components combined using a reduction from \textsc{Unary Bin Packing}. Furthermore, we prove that $k$SC remains NP-hard for graphs with maximum degree three and also graphs with degeneracy two. Finally, we prove that the unweighted $k$SSE is W[1]-hard for the parameter $k$

Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems

A Combined Approach of FMEA and Gray Theory to Rank Aspects of Information Security Risk Management

The study conducted with aim of ranking each aspect of information security risk management. At the first stage, the dimensions and characteristics of each have been identified based on the research literature and expert opinions. In order to rank the factors under study using a hybrid approach using FEMA and Gray theory, 50 questionnaires collected among IT, soft ware, and network experts that choosed based on researchers’ judgement and accessible one. According to the results, the security of communications was ranked first. Infrastructure of hard ware and network, human factors, security management, access to information and systems and the development of secure information systems were ranked second to sixth, respectively.Therefore, it is recommended that organizations set up an independent security department within the organization. Also, providing a list of all the information assets of the organization and specifying control and strategic goals in the area of information security in the organization can be useful for organizations. Moreover, if the organization has several branches and need internet connection, preferably communications are available as VPN. In addition, if organizations have web automation for outside usage, the site should be licensed with SSL and https protocol

An optimized model for open innovation success in manufacturing SMES

Given the fluctuations in markets and the financial and resource constraints of SMEs, innovation is one of the solutions for improving performance, gaining competitive advantage and increasing survival probability for these companies. The paper aims to determine the best ranking of effective factors in open innovation success in manufacturing SMEs. At the first stage, the most important factors investigated using structural equation modelling based on the opinion of 275 experts. Subsequently, the impact level of each factor on the others calculated by fuzzy DEMATEL among 12 specialists’ viewpoints. In the end, optimized ranking of studied factors obtained by Ant Colony Optimization algorithm. As a result, economic factors, suppliers, competitors, partners, firm’s strategy, firm’s structure, reward system, employees, IT support, organizational learning, universities, research institutions, and ecological issues hold the first to the thirteenth rank with the highest cumulative impact on open innovation success. Developing relations with universities and research institutions for improving innovation process is recommended to manufacturing SMEs. In addition, these companies should coordinate firm’s strategy as one of the most important open innovation success factors with partners to gain competitive advantages against competitors

LIPIcs

Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems