University of TehranJournal of Algorithms and Computation2476-277650120180601Sharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs128798910.22059/jac.2018.7989ENR. MuruganandamDepartment of Mathematics, Government Art College,TiruchirappalliR.S. ManikandanDepartment of Mathematics, Bharathidasan University Constituent College, Lalgudi, TiruchirappalliM.Aruvi AruviDepartment of Mathematics, Anna University, Tiruchirappalli, IndiaJournal Article20180330In $1994,$ degree distance of a graph was introduced by Dobrynin<br />, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative version of Gutman index of cartesian product of two connected graphs. And we compute the exact value for the cartesian product of two complete graphs. Using this result, we prove that our bound is tight. Also, we obtain the sharp upper bound for the multiplicative version of degree distance and the multiplicative version of Gutman index of strong product of connected and complete graphs. And we observe the exact value for the strong product of two complete graphs. From this, we prove that our bound is tight.https://jac.ut.ac.ir/article_7989_356861646605b630fbf9fe3d6c43283b.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Improved label propagation algorithms with node attribute and link strength for community detection29506823810.22059/jac.2018.68238ENMohsen ArabYazd universityMahdieh HasheminezhadYazd universityJournal Article20180225Community detection has a wide variety of applications in different fields such as data mining, social network analysis and so on. <br />Label Propagation Algorithm (LPA) is a simple and fast community detection algorithm, but it has low accuracy. There have been presented some advanced versions of LPA in recent years such as CenLP and WILPAS. In this paper, we present improved versions of CenLP and WILPAS methods called CenLP+ and WILPAS+ respectively. Experiments and benchmarks demonstrate that while CenLP+ is as fast as CenLP, it outperforms CenLP on both synthetic and real-world networks. Moreover, while accuracy of WILPAS+ on synthetic networks comparable with that of WILPAS, on real-world networks, WILPAS+ excels WILPAS. In addition, whereas both presented methods CenLP+ and WILPAS+ show high accuracy on synthetic networks, on real-world networks they outperform remarkably all other tested label propagation based algorithms for community detection. Therefore, since CenLP+ and WILPAS+ are both fast and accurate, specially on real-world networks, they can efficiently reveal community structures of mega-scale social networks.https://jac.ut.ac.ir/article_68238_1708e04d7995d0e202872c173eb66567.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Tree Technology for Memory Confidentiality Integrity Protection51676833810.22059/jac.2018.68338ENHui Min MengSchool of Information Science and Engineering, Dalian Polytechnic University, Dalian, China ,116034.HongJin WangSchool of Information Science and Engineering, Dalian Polytechnic University, Dalian, China ,116034.NianMin YaoFauclty of Electronic Information Science and Engineering, Dalian University of Technology, Dalian, China, 116024ShunYi ChengFauclty of Electronic Information Science and Engineering, Dalian University of Technology, Dalian, China, 116024Journal Article20180208PCIP\underline{ }Tree is a Parallelized memory Confidentiality and Integrity Protection technology (PCIP) method that pre-diffuses and encrypts the data stored in off-chip counter value for confidentiality and integrity protection of data, adding redundant checking data to the protection data block to ensure the integrity and confidentiality of the memory data. Then use the Simple Scalar tool to run 10 processors (SPEC2000) benchmark programs to simulation test. The result shows that the PCIP\underline{ }Tree method is greatly improved the running efficiency and the efficiency of encryption methods to compare with the Parallelized Encryption and Integrity Checking Engine (PE-ICE) method, at the same time, through the redundant data to check data integrity is better than using complex Hash algorithm to calculate the checking value and reduce system delay, reduce storage overhead chip, and ensure the real-time encryption and checking.https://jac.ut.ac.ir/article_68338_0a7e4f4334e2402b0b30c24b72ac86b6.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Improper Filter Reduction69996834010.22059/jac.2018.68340ENFatemehzahra SaberifarDepartment of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.Ali MohadesAmirkabir University of TechnologyMohammadreza RazzaziAmirkabir University of TechnologyJason J. M. O'KaneUniversity of South CarolinaJournal Article20180208Combinatorial filters, which are discrete representations of estimation<br />processes, have been the subject of increasing interest from the robotics<br />community in recent years.<br />%<br />This paper considers automatic reduction of combinatorial filters to a given<br />size, even if that reduction necessitates changes to the filter's behavior.<br />%<br />We introduce an algorithmic problem called \emph{improper<br /> filter reduction}, in which the input is a combinatorial filter $F$ along<br />with an integer $k$ representing the target size. The output is another<br />combinatorial filter $F'$ with at most $k$ states, such that the difference<br />in behavior between $F$ and $F'$ is minimal.<br />We present two methods for measuring the distance between pairs of filters, describe dynamic <br />programming algorithms for computing these distances, and<br />show that improper filter reduction is NP-hard under these methods.<br />%<br />We then describe two heuristic algorithms for improper filter reduction, one<br />\changed{greedy sequential} approach, and one randomized global approach based on prior work<br />on weighted improper graph coloring. We have implemented these algorithms<br />and analyze the results of three sets of experiments.https://jac.ut.ac.ir/article_68340_4cb7b0907ca92ebe199a2f85d9a913d3.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601One Modulo Three Geometric Mean Graphs1011086834210.22059/jac.2018.68342ENP. JeyanthiGovindammal Aditanar College for Women Tiruchendur-628 215, Tamil Nadu, India.A. MaheswariDepartment of Mathematics Kamaraj College of Engineering and Technology Virudhunagar- 626 001, Tamil Nadu, IndiaP. PandiarajDepartment of Mathematics Kamaraj College of Engineering and Technology Virudhunagar- 626 001, Tamil Nadu, IndiaJournal Article20180128A graph $G$ is said to be one modulo three geometric mean graph if there is an injective function $\phi$ from the vertex set of $G$ to the set $\{a \mid 1\leq a \leq 3q-2\} $ and either $a\equiv 0(mod 3) $ or $ a\equiv 1(mod 3)\}$ where $q$ is the number of edges of $G$ and $\phi$ induces a bijection $\phi^{*}$ form the edge set of $G$ to $\{a \mid 1\leq a\leq 3q-2 $ and $ a\equiv 1(mod3)\}$ given by $\phi^{*}(uv)=\left\lceil \sqrt{\phi(u)\phi(v)}\right\rceil$ or $\left\lfloor \sqrt{\phi(u)\phi(v)}\right\rfloor$ and the function $\phi$ is called one modulo three geometric mean labeling of $G$. In this paper, we establish that some families of graphs admit one modulo three geometric mean labeling.https://jac.ut.ac.ir/article_68342_e53cdfd892a4cf9b99d51c533e8902a6.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Vulnerability in Networks - A Survey1091186836710.22059/jac.2018.68367ENDara MoazzamiDepartment of Algorithms and Computation, Faculty of Engineering Science, School of Engineering, University of Tehran, Iran,
and
Department of Mathematics, UCLA, California, USAJournal Article20180102The analysis of vulnerability in networks generally involves some questions<br />about how the underlying graph is connected. One is naturally interested<br />in studying the types of disruption in the network that maybe caused<br />by failures of certain links or nodes. In terms of a graph, the concept of<br />connectedness is used in different forms to study many of the measures<br />of vulnerability. When certain vertices or edges of a connected graph<br />are deleted, one wants to know whether the remaining graph is still<br />connected, and if so, what its vertex - or edge - connectivity is. If on the<br />other hand, the graph is disconnected, the determination of the number of<br />its components or their orders is useful. Our purpose here is to describe<br />and analyses the current status of the vulnerability measures, identify its<br />more interesting variants, and suggest a most suitable measure of<br />vulnerability.https://jac.ut.ac.ir/article_68367_d654cd37f3a5b5efa2f7cdae6f35e6c2.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Pointed Conflict-Free Colouring of Digraphs1191316842510.22059/jac.2018.68425ENMahdieh HasheminezhadYazd universityJournal Article20180507In a pointed conflict-free partial (PCFP) colouring of a digraph, each vertex has at least one in-neighbour with unique colour. In this paper, it is proved that PCFP $k$-colourability of digraphs is NP-complete, for any $k >0$. Nevertheless for paths and cycles, one can in linear time find a PCFP colouring with a minimum number of colours and for a given tree, one can find a PCFP 2-colouring. In this paper a bipartite digraph whose arcs start from the same part is called a one-way bipartite digraph. It is proved every one-way bipartite planar digraph has a PCFP 6-colouring, every one-way bipartite planar digraph whose each vertex has in-degree zero or greater than one, has a PCFP 5-colouring and every one-way bipartite planar digraph whose each vertex has in-degree zero or greater than two, has a PCFP 2-colouring. Two simple algorithms are proposed for finding a PCFP colouring of a given digraph such that the number of colours used is not more than the maximum out-degree of the vertices. For a digraph with a given PCFP colouring, it is shown how to recolour the vertices after vertex or arc insertion or deletion to obtain a PCFP colouring for the new digraph.https://jac.ut.ac.ir/article_68425_30d4b1e068528f6d75397022bf311040.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Defining the Tipping Point Based on Conditionally Convergent Series: Explaining the Indeterminacy1331426863010.22059/jac.2018.68630ENMohammad Hosseini MoghaddamACECR, Institute for Humanities and Social SciencesTahmineh SahverdiACECR, Institute for Humanities and Social SciencesJournal Article20180112Tipping Point refers to the moment when an adaption or infection sustains itself in network without further external inputs. Until now, studies have mainly focused on the occurrence of the Tipping Point and what it leads to rather than what precedes it. This paper explores the situation leading to the Tipping Point during a process of diffusion in networks. The core of the debate is to manifest that the process can be introduced as an example of conditionally convergent series and that determining the tipping points’ occurrence is conditional to the arrangement of the series based on Reimann Rearrangement Theorem. Accordingly, the occurrence of curve does not follow a general formulation. That is called indeterminacy since that the predictions about tipping points for any diffusion over the network may include a variety of right answers, although such indeterminacy neither means there is no tipping point nor many.https://jac.ut.ac.ir/article_68630_8c0a9cd094be42ea9ddb0cdc693c0d32.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601$k$-Total prime cordial labeling of graphs1431496865110.22059/jac.2018.68651ENR PonrajDepartment of Mathematics,
Sri Paramakalyani College,
Alwarkurichi-627412J MaruthamaniResearch Scholar,
Department of Mathematics
Manonmaniam sundarnar university, Abishekapatti,
Tirunelveli-627 012,
Tamilnadu, India.R KalaDepartment of Mathematics,
Manonmaniam sundarnar university, Abishekapatti,
Tirunelveli-627 012, Tamilnadu, India.Journal Article20180207In this paper we introduce a new graph labeling method called $k$-Total prime cordial. Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to\{1,2, \ldots, k\}$ be a map where $k \in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $\left|t_{f}(i)-t_{f}(j)\right|\leq 1$, $i,j \in \{1,2, \ldots, k\}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labeled with $x$. We investigate k-total prime cordial labeling of some graphs and study the 4-total prime cordial labeling of path, cycle, complete graph etc.https://jac.ut.ac.ir/article_68651_1dc2872652857fc9a585a106b9f4f744.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Novel Computation of Algorithmic Geometric Series and Summability1511536886610.22059/jac.2018.68866ENChinnaraji AnnamalaiIndian Institute of Technology KharagpurJournal Article20170829This paper presents a new mathematical technique for computation of geometric series and summability. This technique uses Annamalai’s computing model of algorithmic geometric series and its mathematical structures for further development of the infinite geometric series and summability. This could be very interesting and informative for current students and researchers.In the research study, a novel technique has been presented for formation and computation of infinite geometric series and summability.https://jac.ut.ac.ir/article_68866_c35c9a752fb0e8678fbed5678de77932.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Solving a non-linear optimization problem in the presence of Yager-FRE constraints1551836896410.22059/jac.2018.68964ENA. GhodousianUniversity of Tehran, College of Engineering, Faculty of Engineering Science0000-0002-9224-8470Abolfazl JavanUniversity of Tehran-
Department of Algorithms and Computation
Tehran-IranAsieh KhoshnoodUniversity of Tehran
Department of Algorihthms and Computation, Tehran, IranJournal Article20180112Yager family of t-norms is a parametric family of continuous nilpotent t-norms which is also one of the most frequently applied one. This family of t-norms is strictly increasing in its parameter and covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Yager t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Yager composition and present some necessary and sufficient conditions for determining the feasibility and some procedures for simplifying the problem. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional nonlinear programming methods may involve high computation complexity. For these reasons, a method is used, which preserves the feasibility of new generated solutions. The proposed method does not need to initially find the minimal solutions. Also, it does not need to check the feasibility after generating the new solutions. Moreover, we present a technique to generate feasible max-Yager FREs as test problems for evaluating the performance of the current algorithm. The proposed method has been compared with Lu and Fang’s algorithm. The obtained results confirm the high performance of the proposed method in solving such nonlinear problems.https://jac.ut.ac.ir/article_68964_cc2c1a89bfe91826624e923899270238.pdfUniversity of TehranJournal of Algorithms and Computation2476-277650120180601Vertex Switching in 3-Product Cordial Graphs1851886896510.22059/jac.2018.68965ENP. JeyanthiPrincipal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIAA. MaheswariDepartment of Mathematics,
Kamaraj College of Engineering and Technology,
Virudhunagar, India.M. VijayaLakshmiDepartment of Mathematics, Dr.G.U. Pope College of Engineering, Sawyerpuram,Thoothukudi District, Tamil Nadu, IndiaJournal Article20180123A mapping $f: V(G)\rightarrow\left\{0, 1, 2 \right\}$ is called 3-product cordial labeling if $\vert v_f(i)-v_f(j)\vert \leq 1$ and $\vert e_f(i)-e_f(j)\vert \leq 1$ for any $ i, j\in \{0, 1, 2\}$, where $v_f(i)$ denotes the number of vertices labeled with $i, e_f (i)$ denotes the number of edges $xy$ with $f(x)f(y)\equiv i(mod \ 3)$. A graph with 3-product cordial labeling is called 3-product cordial graph. In this paper we establish that vertex switching of wheel,gear graph and degree splitting of bistar are 3-product cordial graphs.https://jac.ut.ac.ir/article_68965_8b071b3e1293e051be82e794596f567c.pdf