eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-01
47
1
1
10
361
3-difference cordial labeling of some cycle related graphs
R. Ponraj
ponrajmaths@gmail.com
1
M. Maria Adaickalam
mariaadaickalam@gmail.com
2
Department of Mathematics, Sri Paramakalyani College,Alwarkurichi-627 412, India
Department of Mathematics, Kamarajar Government Arts College, Surandai-627859, India
Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-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.
http://jac.ut.ac.ir/pdf_361_2058a8520b6be55a66b6d88cf1ff676f.html
Path
Cycle
wheel
Star
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-01
47
1
11
19
365
A Survey on Complexity of Integrity Parameter
Mahmood Shabankhah
shabankhah@ut.ac.ir
1
University of Tehran, College of Engineering, Department of Engineering Science
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 G, I(G), is defined to be min(| S | +m(G − S)) where S ⊂ V (G) and m(G − S) is the maximum order of the components of G − S. Similarly the edge-integrity of G is I′(G) := min(| S | +m(G − S)) where now S ⊆ E(G). Here and through the remaining sections, by an I-set (with respect to some prescribed graph G) we will mean a set S ⊂ V (G) for which I(G) =| S | +m(G − S). We define an I′-set similarly. In this paper we show a lower bound on the edgeintegrity of graphs and present an algorithm for its computation.
http://jac.ut.ac.ir/pdf_365_cbdf47ab50798add111a36ddb52c43be.html
Integrity parameter
toughness
neighborconnectivity
mean integrity
edge-connectivity vector
l-connectivity and tenacity
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-02
47
1
21
26
366
On Generalized Weak Structures
R. Jamunarani
jamunarani1977@gmail.com
1
P. Jeyanthi
jeyajeyanthi@rediffmail.com
2
T. Noiri
t.noiri@nifty.com
3
Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India
Research Center, Department of Mathematics, Govindammal Aditanar College for Women, Tiruchendur-628 215, Tamil Nadu, India
Shiokota-cho Hinagu, Yatsushiro-shi kumamoto-ken, 869-5142 Japan
Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures ro(g), rc(g), and also further properties of α(g),π(g),σ(g) and β(g) due to [1].
http://jac.ut.ac.ir/pdf_366_9e73174a81cdfca4a7d711bd908dca2a.html
Generalized weak structure
ro(g)
rc(g)
α(g)
π(g)
σ(g)
β(g)
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-01
47
1
27
36
367
Online Scheduling of Jobs for D-benevolent instances On Identical Machines
I. Mohammadi
mohammadi.iman@alumni.ut.ac.ir
1
Dara Moazzami
dmoazzami@ut.ac.ir
2
University of Tehran, Department of Algorithms and Computation.
University of Tehran, College of Engineering, Faculty of Engineering Science
We consider online scheduling of jobs with specic release time on m 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 D-benevolent instances which is a wide and standard class and we give a new algorithm, that admits (2m + 4)-competitive ratio. It is almost half of the previous known upper bound for this problem.
http://jac.ut.ac.ir/pdf_367_f66b689563341f19f8abe5d5de8da400.html
Online Algorithms Scheduling Identical Machine
Upper bound
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-01
47
1
37
52
368
Mixed cycle-E-super magic decomposition of complete bipartite graphs
G. Marimuthu
yellowmuthu@yahoo.com;
1
S. Stalin Kumar
sskumbas@gmail.com
2
Department of Mathematics, The Madura College, Madurai -625 011, Tamilnadu, India
Department of Mathematics, The American College, Madurai - 625 002, Tamilnadu,India
An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) + ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ 3, E(Hi) ∩ E(Hj) = ∅ for i ≠ j and ∪hi=1E(Hi) = E(G). In this paper, we prove that K2m,2n is mixed cycle-E-super magic decomposable where m ≥ 2, n ≥ 3, with the help of the results found in [1].
http://jac.ut.ac.ir/pdf_368_5f537569fcfee7d3d929abdef859d33f.html
H-decomposable graph
H-E-super magic labeling
mixed cycle-E-super magic decomposable graph
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-03-19
47
1
53
62
370
Heuristic and exact algorithms for Generalized Bin Covering Problem
S. Jabari
sjabari@ut.ac.ir
1
Dara Moazzami
dmoazzami@ut.ac.ir
2
A. Ghodousian
a.ghodousian@ut.ac.ir
3
University of Tehran, Department of Algorithms and Computation.
University of Tehran, College of Engineering, Faculty of Engineering Science
University of Tehran, College of Engineering, Faculty of Engineering Science
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.
http://jac.ut.ac.ir/pdf_370_ead5452fc8136548321a56c8bfa77888.html
Generalized Bin Covering Problem
heuristic algorithm
greedy algorithm
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-06-10
47
1
63
78
377
Zarankiewicz Numbers and Bipartite Ramsey Numbers
Alex F. Collins
weincoll@gmail.com
1
Alexander W. N. Riasanovsky
alexneal@math.upenn.edu
2
John C. Wallace
john.wallace@trincoll.edu
3
Stanis law P. Radziszowski
spr@cs.rit.edu
4
Rochester Institute of Technology, School of Mathematical Sciences, Rochester, NY 14623
University of Pennsylvania, Department of Mathematics, Philadelphia, PA 19104, USA
Trinity College, Department of Mathematics, Hartford, CT 06106, USA
Rochester Institute of Technology, Department of Computer Science, Rochester, NY 14623
The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.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 z(b; s) for 3≤s≤6. Our approach and new knowledge about z(b; s) permit us to improve some of the results on bipartite Ramsey numbers obtained by
http://jac.ut.ac.ir/pdf_377_0d5d2a7f40f78dfe0e529df98f3049dd.html
Zarankiewicz number
bipartite Ramsey number
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-04-01
47
1
79
92
378
Randomized Algorithm For 3-Set Splitting Problem and it's Markovian Model
Mahdi Heidari
mahdi.heydari@intec.ugent.be
1
Ali Golshani
ali.golshani@gmail.com
2
D. Moazzami
dmoazzami@ut.ac.ir
3
Ali Moeini
moeini@ut.ac.ir
4
Department of Algorithms and Computation, University of Tehran
Department of Algorithms and Computation, University of Tehran
University of Tehran, College of Engineering, Faculty of Enginering Science
University of Tehran, College of Engineering, Faculty of Enginering Science
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.
http://jac.ut.ac.ir/pdf_378_cf76fdb4b0ab6812faebfef5f611d4d6.html
NP-complete problem
set splitting problem
SAT problem
Markov chain
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-03-24
47
1
93
99
381
A Cellular Automaton Based Algorithm for Mobile Sensor Gathering
S. Saadatmand
samadseadatmand@yahoo.com
1
D. Moazzami
dmoazzami@ut.ac.ir
2
A. Moeini
moeini@ut.ac.ir
3
University of New South Wales, College of Engineering, Department of Computer Science, Sydney, Australia.
University of Tehran, College of Engineering, Faculty of Engineering Science
University of Tehran, College of Engineering, Faculty of Engineering Science
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.
http://jac.ut.ac.ir/pdf_381_1aea8cc39be37b7a09b0e9f9f6aa0812.html
Mobile Wireless Sensor Network
Mobile Sensor Gathering
Cellular Automata
Local Algorithm
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-04-01
47
1
101
117
383
A Mathematical Optimization Model for Solving Minimum Ordering Problem with Constraint Analysis and some Generalizations
Samira Rezaei
samirarezaei@ut.ac.ir
1
Amin Ghodousian
a.ghodousian@ut.ac.ir
2
Department of Algorithms and Computation, University of Tehran
University of Tehran, College of Engineering, Faculty of Engineering Science
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.
http://jac.ut.ac.ir/pdf_383_b3e9bb57657183c34d60a4df9921c654.html
linear programming
integer programming
minimum ordering
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-05-01
47
1
119
125
384
The edge tenacity of a split graph
Bahareh Bafandeh Mayvan
bahareh.bafandeh@gmail.com
1
Department of Computer Engineering, Ferdowsi University of Mashhad
The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split graph with minimum vertex degree δ(G) we prove that if δ(G)≥|E(G)|/[|V(G)|-1] then its edge-tenacity is |E(G)|/[|V(G)|-1] .
http://jac.ut.ac.ir/pdf_384_79987a74d7a89e4dc593ea40d6df17ea.html
Vertex degree
split graphs
edge tenacity
eng
University of Tehran
Journal of Algorithms and Computation
2776-2476
2476-2784
2016-05-21
47
1
127
135
385
Minimum Tenacity of Toroidal graphs
Hamid Doost Hosseini
h.doosth@gmail.com
1
University of Tehran, College of Engineering, School of Civil Engineering
The tenacity of a graph G, T(G), is dened by T(G) = min{[|S|+τ(G-S)]/[ω(G-S)]}, where the minimum is taken over all vertex cutsets S of G. We dene τ(G - S) to be the number of the vertices in the largest component of the graph G - S, and ω(G - S) be the number of components of G - S.In this paper a lower bound for the tenacity T(G) of a graph with genus γ(G) is obtained using the graph's connectivity κ(G). Then we show that such a bound for almost all toroidal graphs is best possible.
http://jac.ut.ac.ir/pdf_385_c8ea937acc51627d689d94f03167568d.html
genus
graph's connectivity
toroidal graphs