University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
01
3-difference cordial labeling of some cycle related graphs
1
10
EN
R.
Ponraj
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
ponrajmaths@gmail.com
M.
Maria Adaickalam
Department of Mathematics, Kamarajar Government Arts College, Surandai-627859, India
mariaadaickalam@gmail.com
Let <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.
Path,cycle,Wheel,Star
https://jac.ut.ac.ir/article_7927.html
https://jac.ut.ac.ir/article_7927_2058a8520b6be55a66b6d88cf1ff676f.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
01
A Survey on Complexity of Integrity Parameter
11
19
EN
Mahmood
Shabankhah
University of Tehran, College of Engineering, Department of Engineering Science
shabankhah@ut.ac.ir
Many 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.
Integrity parameter,toughness,neighborconnectivity,mean integrity,edge-connectivity vector,l-connectivity and tenacity
https://jac.ut.ac.ir/article_7931.html
https://jac.ut.ac.ir/article_7931_cbdf47ab50798add111a36ddb52c43be.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
02
On Generalized Weak Structures
21
26
EN
R.
Jamunarani
Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India
jamunarani1977@gmail.com
P.
Jeyanthi
Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India
jeyajeyanthi@rediffmail.com
T.
Noiri
Shiokota-cho Hinagu, Yatsushiro-shi kumamoto-ken, 869-5142 Japan
t.noiri@nifty.com
Avila 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].
Generalized weak structure,ro(g),rc(g),α(g),π(g),σ(g),β(g)
https://jac.ut.ac.ir/article_7932.html
https://jac.ut.ac.ir/article_7932_9e73174a81cdfca4a7d711bd908dca2a.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
01
Online Scheduling of Jobs for D-benevolent instances On Identical Machines
27
36
EN
I.
Mohammadi
University of Tehran, Department of Algorithms and Computation.
mohammadi.iman@alumni.ut.ac.ir
Dara
Moazzami
University of Tehran, College of Engineering, Faculty of Engineering Science
dmoazzami@ut.ac.ir
We 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.
Online Algorithms Scheduling Identical Machine,Upper bound
https://jac.ut.ac.ir/article_7933.html
https://jac.ut.ac.ir/article_7933_f66b689563341f19f8abe5d5de8da400.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
01
Mixed cycle-E-super magic decomposition of complete bipartite graphs
37
52
EN
G.
Marimuthu
Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India
yellowmuthu@yahoo.com;
S.
Stalin Kumar
Department of Mathematics, The American College, Madurai - 625 002, Tamilnadu,India
sskumbas@gmail.com
An 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].
H-decomposable graph,H-E-super magic labeling,mixed cycle-E-super magic decomposable graph
https://jac.ut.ac.ir/article_7934.html
https://jac.ut.ac.ir/article_7934_5f537569fcfee7d3d929abdef859d33f.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
03
19
Heuristic and exact algorithms for Generalized Bin Covering Problem
53
62
EN
S.
Jabari
University of Tehran, Department of Algorithms and Computation.
sjabari@ut.ac.ir
Dara
Moazzami
University of Tehran, College of Engineering, Faculty of Engineering Science
dmoazzami@ut.ac.ir
A.
Ghodousian
University of Tehran, College of Engineering, Faculty of Engineering Science
a.ghodousian@ut.ac.ir
In 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.
Generalized Bin Covering Problem,heuristic algorithm,greedy algorithm
https://jac.ut.ac.ir/article_7936.html
https://jac.ut.ac.ir/article_7936_ead5452fc8136548321a56c8bfa77888.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
06
10
Zarankiewicz Numbers and Bipartite Ramsey Numbers
63
78
EN
Alex F.
Collins
Rochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623
weincoll@gmail.com
Alexander W. N.
Riasanovsky
University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USA
alexneal@math.upenn.edu
John C.
Wallace
Trinity College, Department of Mathematics, Hartford, CT 06106, USA
john.wallace@trincoll.edu
Stanis law P.
Radziszowski
Rochester Institute of Technology, Department of Computer Science, Rochester, NY 14623
spr@cs.rit.edu
The 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 by
Zarankiewicz number,bipartite Ramsey number
https://jac.ut.ac.ir/article_7943.html
https://jac.ut.ac.ir/article_7943_0d5d2a7f40f78dfe0e529df98f3049dd.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
04
01
Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model
79
92
EN
Mahdi
Heidari
Department of Algorithms and Computation, University of Tehran
mahdi.heydari@intec.ugent.be
Ali
Golshani
Department of Algorithms and Computation, University of Tehran
ali.golshani@gmail.com
D.
Moazzami
University of Tehran, College of Engineering, Faculty of Enginering Science
dmoazzami@ut.ac.ir
Ali
Moeini
University of Tehran, College of Engineering, Faculty of Enginering Science
moeini@ut.ac.ir
In 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.
NP-complete problem,set splitting problem,SAT problem,Markov chain
https://jac.ut.ac.ir/article_7944.html
https://jac.ut.ac.ir/article_7944_cf76fdb4b0ab6812faebfef5f611d4d6.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
03
24
A Cellular Automaton Based Algorithm for Mobile Sensor Gathering
93
99
EN
S.
Saadatmand
University of New South Wales, College of Engineering, Department of Computer Science, Sydney, Australia.
samadseadatmand@yahoo.com
D.
Moazzami
University of Tehran, College of Engineering, Faculty of Engineering Science
dmoazzami@ut.ac.ir
A.
Moeini
University of Tehran, College of Engineering, Faculty of Engineering Science
moeini@ut.ac.ir
In 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.
Mobile Wireless Sensor Network,Mobile Sensor Gathering,Cellular Automata,Local Algorithm
https://jac.ut.ac.ir/article_7947.html
https://jac.ut.ac.ir/article_7947_1aea8cc39be37b7a09b0e9f9f6aa0812.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
04
01
A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations
101
117
EN
Samira
Rezaei
Department of Algorithms and Computation, University of Tehran
samirarezaei@ut.ac.ir
Amin
Ghodousian
University of Tehran, College of Engineering, Faculty of Engineering Science
a.ghodousian@ut.ac.ir
In 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.
linear programming,integer programming,minimum ordering
https://jac.ut.ac.ir/article_7949.html
https://jac.ut.ac.ir/article_7949_b3e9bb57657183c34d60a4df9921c654.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
05
01
The edge tenacity of a split graph
119
125
EN
Bahareh
Bafandeh Mayvan
Department of Computer Engineering, Ferdowsi University of Mashhad
bahareh.bafandeh@gmail.com
The 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] .
Vertex degree,split graphs,edge tenacity
https://jac.ut.ac.ir/article_7950.html
https://jac.ut.ac.ir/article_7950_79987a74d7a89e4dc593ea40d6df17ea.pdf
University of Tehran
Journal of Algorithms and Computation
2476-2776
2476-2784
47
1
2016
05
21
Minimum Tenacity of Toroidal graphs
127
135
EN
Hamid
Doost Hosseini
University of Tehran, College of Engineering, School of Civil Engineering
h.doosth@gmail.com
The 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.
genus,graph's connectivity,toroidal graphs
https://jac.ut.ac.ir/article_7951.html
https://jac.ut.ac.ir/article_7951_c8ea937acc51627d689d94f03167568d.pdf