University of TehranJournal of Algorithms and Computation2476-2776471201606013-difference cordial labeling of some cycle related graphs110792710.22059/jac.2016.7927ENR.PonrajDepartment of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, IndiaM.Maria AdaickalamDepartment of Mathematics, Kamarajar Government Arts College, Surandai-627859, IndiaJournal Article20151020Let <em>G</em> be a (<em>p</em>, <em>q</em>) graph. Let <em>k</em> be an integer with 2 ≤ <em>k</em> ≤ <em>p</em> and <em>f</em> from <em>V</em> (<em>G</em>) to the set {1, 2, . . . , <em>k</em>} be a map. For each edge <em>uv</em>, assign the label |<em>f</em>(<em>u</em>) − <em>f</em>(<em>v</em>)|. The function <em>f</em> is called a <em>k</em>-difference cordial labeling of <em>G</em> if |<em>ν<sub>f</sub></em> (<em>i</em>) − <em>v<sub>f</sub></em> (<em>j</em>)| ≤ 1 and |<em>e<sub>f</sub></em> (0) − <em>e<sub>f</sub></em> (1)| ≤ 1 where <em>v<sub>f</sub></em> (<em>x</em>) denotes the number of vertices labelled with <em>x</em> (<em>x</em> ∈ {1, 2 . . . , <em>k</em>}), <em>e<sub>f</sub></em> (1) and <em>e<sub>f</sub></em> (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a <em>k</em>-difference cordial labeling is called a <em>k</em>-difference cordial graph. In this paper we investigate the 3-difference cordial labeling of wheel, helms, flower graph, sunflower graph, lotus inside a circle, closed helm, and double wheel.https://jac.ut.ac.ir/article_7927_2058a8520b6be55a66b6d88cf1ff676f.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160601A Survey on Complexity of Integrity Parameter1119793110.22059/jac.2016.7931ENMahmoodShabankhahUniversity of Tehran, College of Engineering, Department of Engineering ScienceJournal Article20150510Many graph theoretical parameters have been used to describe the vulnerability of communication networks, including toughness, binding number, rate of disruption, neighbor-connectivity, integrity, mean integrity, edgeconnectivity vector, l-connectivity and tenacity. In this paper we discuss Integrity and its properties in vulnerability calculation. The integrity of a graph <em>G</em>, <em>I</em>(<em>G</em>), is defined to be min(| <em>S</em> | +<em>m</em>(<em>G</em> −<em> S</em>)) where <em>S</em> ⊂ <em>V</em> (<em>G</em>) and <em>m</em>(<em>G</em> − <em>S</em>) is the maximum order of the components of <em>G</em> − <em>S</em>. Similarly the edge-integrity of <em>G</em> is <em>I′</em>(<em>G</em>) := min(| <em>S</em> | +<em>m</em>(<em>G</em> − <em>S</em>)) where now <em>S</em> ⊆ <em>E</em>(<em>G</em>). Here and through the remaining sections, by an <em>I</em>-set (with respect to some prescribed graph <em>G</em>) we will mean a set <em>S</em> ⊂ <em>V</em> (<em>G</em>) for which <em>I</em>(<em>G</em>) =| <em>S</em> | +<em>m</em>(<em>G</em> − <em>S</em>). We define an<em> I′</em>-set similarly. <br />In this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation.https://jac.ut.ac.ir/article_7931_cbdf47ab50798add111a36ddb52c43be.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160602On Generalized Weak Structures2126793210.22059/jac.2016.7932ENR.JamunaraniResearch Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, IndiaP.JeyanthiResearch Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, IndiaT.NoiriShiokota-cho Hinagu, Yatsushiro-shi kumamoto-ken, 869-5142 JapanJournal Article20151201Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures <em>α</em>(<em>g</em>),<em>π</em>(<em>g</em>),<em>σ</em>(<em>g</em>) and <em>β</em>(<em>g</em>). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures <em>ro</em>(<em>g</em>) and <em>rc</em>(<em>g</em>) and study the properties of the structures <em>ro</em>(<em>g</em>), <em>rc</em>(<em>g</em>), and also further properties of <em>α</em>(<em>g</em>),<em>π</em>(<em>g</em>),<em>σ</em>(<em>g</em>) and <em>β</em>(<em>g</em>) due to [1].https://jac.ut.ac.ir/article_7932_9e73174a81cdfca4a7d711bd908dca2a.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160601Online Scheduling of Jobs for D-benevolent instances On Identical Machines2736793310.22059/jac.2016.7933ENI.MohammadiUniversity of Tehran, Department of Algorithms and Computation.DaraMoazzamiUniversity of Tehran, College of Engineering, Faculty of Engineering ScienceJournal Article20150320We consider online scheduling of jobs with specic release time on <em>m</em> identical machines. Each job has a weight and a size; the goal is maximizing total weight of completed jobs. At release time of a job it must immediately be scheduled on a machine or it will be rejected. It is also allowed during execution of a job to preempt it; however, it will be lost and only weight of completed jobs contribute on prot of the algorithm. In this paper we study <em>D</em>-benevolent instances which is a wide and standard class and we give a new algorithm, that admits (2<em>m</em> + 4)-competitive ratio. It is almost half of the previous known upper bound for this problem.https://jac.ut.ac.ir/article_7933_f66b689563341f19f8abe5d5de8da400.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160601Mixed cycle-E-super magic decomposition of complete bipartite graphs3752793410.22059/jac.2016.7934ENG.MarimuthuDepartment of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, IndiaS.Stalin KumarDepartment of Mathematics, The American College, Madurai - 625 002, Tamilnadu,IndiaJournal Article20151020An H-magic labeling in a <em>H</em>-decomposable graph <em>G</em> is a bijection<em> f</em> : <em>V</em> (<em>G</em>) ∪ <em>E</em>(<em>G</em>) → {1, 2, ..., <em>p</em> + <em>q</em>} such that for every copy <em>H</em> in the decomposition, Σ<sub><em>ν</em>ε<em>V</em>(<em>H</em>)</sub> <em>f</em>(<em>v</em>) + Σ<sub><em>e</em>ε<em>E</em>(<em>H</em>)</sub> <em>f</em>(<em>e</em>) is constant. <em>f</em> is said to be <em>H</em>-<em>E</em>-super magic if <em>f</em>(<em>E</em>(<em>G</em>)) = {1, 2, · · · , <em>q</em>}. A family of subgraphs <em>H</em><sub>1</sub>,<em>H</em><sub>2</sub>, · · · ,<em>H<sub>h</sub></em> of <em>G</em> is a mixed cycle-decomposition of <em>G</em> if every subgraph <em>H<sub>i</sub></em> is isomorphic to some cycle<em> C<sub>k</sub></em>, for <em>k</em> ≥ 3, <em>E</em>(<em>H<sub>i</sub></em>) ∩ <em>E</em>(<em>H<sub>j</sub></em>) = ∅ for <em>i</em> ≠<em> j</em> and ∪<em><sup>h</sup></em><sub><em>i</em>=1</sub><em>E</em>(<em>H<sub>i</sub></em>) = <em>E</em>(<em>G</em>). In this paper, we prove that <em>K</em><sub>2<em>m</em>,2<em>n</em></sub> is mixed cycle-E-super magic decomposable where <em>m</em> ≥ 2, <em>n</em> ≥ 3, with the help of the results found in [1].https://jac.ut.ac.ir/article_7934_5f537569fcfee7d3d929abdef859d33f.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160319Heuristic and exact algorithms for Generalized Bin Covering Problem5362793610.22059/jac.2016.7936ENS.JabariUniversity of Tehran, Department of Algorithms and Computation.DaraMoazzamiUniversity of Tehran, College of Engineering, Faculty of Engineering ScienceA.GhodousianUniversity of Tehran, College of Engineering, Faculty of Engineering ScienceJournal Article20151020In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.https://jac.ut.ac.ir/article_7936_ead5452fc8136548321a56c8bfa77888.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160610Zarankiewicz Numbers and Bipartite Ramsey Numbers6378794310.22059/jac.2016.7943ENAlex F.CollinsRochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623Alexander W. N.RiasanovskyUniversity of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USAJohn C.WallaceTrinity College, Department of Mathematics, Hartford, CT 06106, USAStanis Law P.RadziszowskiRochester Institute of Technology, Department of Computer Science, Rochester, NY 14623Journal Article20160208The Zarankiewicz number <em>z</em>(<em>b;</em> <em>s</em>) is the maximum size of a subgraph of <em>K</em><sub><em>b</em>,<em>b</em></sub> which does not contain <em>K</em><sub><em>s</em>,<em>s</em></sub> as a subgraph. The two-color bipartite Ramsey number <em>b</em>(<em>s</em>, <em>t</em>) is the smallest integer <em>b</em> such that any coloring of the edges of <em>K</em><sub><em>b</em>,<em>b</em></sub> with two colors contains a <em>K</em><sub><em>s</em>,<em>s</em></sub> in the rst color or a <em>K</em><sub><em>t</em>,<em>t</em></sub> in the second color.<br />In this work, we design and exploit a computational method for bounding and computing Zarankiewicz numbers. Using it, we obtain several new values and bounds on <em>z</em>(<em>b;</em> <em>s</em>) for 3≤s≤6. Our approach and new knowledge about <em>z</em>(<em>b;</em> <em>s</em>) permit us to improve some of the results on bipartite Ramsey numbers obtained byhttps://jac.ut.ac.ir/article_7943_0d5d2a7f40f78dfe0e529df98f3049dd.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160401Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model7992794410.22059/jac.2016.7944ENMahdiHeidariDepartment of Algorithms and Computation, University of TehranAliGolshaniDepartment of Algorithms and Computation, University of TehranD.MoazzamiUniversity of Tehran, College of Engineering, Faculty of Enginering ScienceAliMoeiniUniversity of Tehran, College of Engineering, Faculty of Enginering Science0000-0003-4593-3018Journal Article20150630In this paper we restrict every set splitting problem to the special case in which every set has just three elements. This restricted version is also NP-complete. Then, we introduce a general conversion from any set splitting problem to 3-set splitting. Then we introduce a randomize algorithm, and we use Markov chain model for run time complexity analysis of this algorithm. In the last section of this paper we introduce "Fast Split" algorithm.https://jac.ut.ac.ir/article_7944_cf76fdb4b0ab6812faebfef5f611d4d6.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160324A Cellular Automaton Based Algorithm for Mobile Sensor Gathering9399794710.22059/jac.2016.7947ENS.SaadatmandUniversity of New South Wales, College of Engineering, Department of Computer Science, Sydney, Australia.D.MoazzamiUniversity of Tehran, College of Engineering, Faculty of Engineering ScienceA.MoeiniUniversity of Tehran, College of Engineering, Faculty of Engineering Science0000-0003-4593-3018Journal Article20150320In this paper we proposed a Cellular Automaton based local algorithm to solve the autonomously sensor gathering problem in Mobile Wireless Sensor Networks (MWSN). In this problem initially the connected mobile sensors deployed in the network and goal is gather all sensors into one location. The sensors decide to move only based on their local information. Cellular Automaton (CA) as dynamical systems in which space and time are discrete and rules are local, is proper candidate to simulate and analyze the problem. Using CA presents a better understanding of the problem.https://jac.ut.ac.ir/article_7947_1aea8cc39be37b7a09b0e9f9f6aa0812.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160401A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations101117794910.22059/jac.2016.7949ENSamiraRezaeiDepartment of Algorithms and Computation, University of TehranAminGhodousianUniversity of Tehran, College of Engineering, Faculty of Engineering ScienceJournal Article20150530In this paper, a mathematical method is proposed to formulate a generalized ordering problem. This model is formed as a linear optimization model in which some variables are binary. The constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. On the one hand, these constraints enforce conditions on an arbitrary subgraph and then give sufficient conditions for feasibility, on the other hand, they provide a natural way to generalize the applied aspects of the model without increasing the number of the binary variables.https://jac.ut.ac.ir/article_7949_b3e9bb57657183c34d60a4df9921c654.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160501The edge tenacity of a split graph119125795010.22059/jac.2016.7950ENBaharehBafandeh MayvanDepartment of Computer Engineering, Ferdowsi University of MashhadJournal Article20150630The edge tenacity T<sub><em>e</em></sub>(<em>G</em>) of a graph <em>G</em> is dened as:<br />T<sub><em>e</em></sub>(G) = min {[|<em>X</em>|+<em>τ</em>(<em>G</em>-<em>X</em>)]/[<em>ω</em>(<em>G</em>-<em>X</em>)-1]|<em>X</em> <span>⊆</span><span><em> E</em>(<em>G</em>) and<em> ω</em>(<em>G</em>-<em>X</em>) > 1}</span> <br />where the minimum is taken over every edge-cutset <em>X</em> that separates <em>G</em> into <em>ω</em>(<em>G</em> - <em>X</em>) components, and by <em>τ</em>(<em>G</em> -<em> X</em>) we denote the order of a largest component of <em>G</em>. The objective of this paper is to determine this quantity for split graphs. Let <em>G</em> = (<em>Z</em>; <em>I</em>; <em>E</em>) be a noncomplete connected split graph with minimum vertex degree <em>δ</em>(<em>G</em>) we prove that if <em>δ</em>(<em>G</em>)≥|<em>E</em>(<em>G)</em>|/[|<em>V</em>(<em>G</em>)|-1] then its edge-tenacity is |<em>E</em>(<em>G)</em>|/[|<em>V</em>(<em>G</em>)|-1] .https://jac.ut.ac.ir/article_7950_79987a74d7a89e4dc593ea40d6df17ea.pdfUniversity of TehranJournal of Algorithms and Computation2476-277647120160521Minimum Tenacity of Toroidal graphs127135795110.22059/jac.2016.7951ENHamidDoost HosseiniUniversity of Tehran, College of Engineering, School of Civil EngineeringJournal Article20150430The tenacity of a graph <em>G</em>,<em> T</em>(<em>G</em>), is dened by <em>T</em>(<em>G</em>) = min{[|<em>S</em>|+<em>τ</em>(<em>G</em>-<em>S</em>)]/[<em>ω</em>(<em>G</em>-<em>S</em>)]}, where the minimum is taken over all vertex cutsets<em> S</em> of <em>G</em>. We dene <em>τ</em>(<em>G</em> - <em>S</em>) to be the number of the vertices in the largest component of the graph <em>G</em> -<em> S</em>, and <em>ω</em>(<em>G</em> - <em>S</em>) be the number of components of <em>G</em> - <em>S</em>.In this paper a lower bound for the tenacity <em>T</em>(<em>G</em>) of a graph with genus <em>γ</em>(<em>G</em>) is obtained using the graph's connectivity <em>κ</em>(<em>G</em>). Then we show that such a bound for almost all toroidal graphs is best possible.https://jac.ut.ac.ir/article_7951_c8ea937acc51627d689d94f03167568d.pdf