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Register a new userA optimization algorithm for determining the thickness of complete graphs and complete bipartite graphs
خوارزمية أمثلية لتحديد ثخانة البيان التام والثنائي التام
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Aِl-Baath University ورقة بحثية
Publication date
2014
fields
Informatics Engineering
and research's language is
العربية
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Shamra Editor
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نرمز نظرياً لثخانة البيان G ب( Φ(G وتعرف ثخانة البيان بأنها العدد الأصغري من البيانات الجزئية المسطحة(المستوية ) والتي نستطيع الحصول عليها من تحميل البيان الأصلي G والبيان المسطح هو كل بيان يمكن إعادة رسمه في المستوي بدون أن تتقاطع أضلاعه (خطوط التوصيّل بين الر ؤوس)، لذلك عرفت مسألة تحديد ثخانة البيان كمسألة تنتمي إلى صف المسائل .NP-complete سنقدم في هذا البحث تطبيقاً لخوارزمية تجريبية Heuristic Algorithm تعتمد على مفهوم محاكاة تلدين الفلزات الأمثلScheme Simulated Annealing Optimization New- hick الذي يساعد في تحسين نتائج الخوارزمية التجريبية المقترحة حيث أعطى حلاً فعالاً وسريعاً في إيجاد ثخانة البيانات التامة والثنائية التامة عندما يكون عدد رؤوس البيان n<=30 وأبطأ عندما يكون أكبر من ذلك. أخيرا نعرض نتائج تطبيق هذه الخوارزمية على الخوارزمية التجريبية فنلاحظ بأنها أعطت حلاً أمثلياً لتحديد ثخانة البيانات التامة والثنائية التامة. كما تمّت برمجة هذه الخوارزمية باستخدام لغة عالية المستوى ++C بمفهوم غرضي التوجه وقد حصلنا على النتائج بتنفيذ البرنامج على حاسوب بمواصفات RAM 2GB, CPU, M350 2.27GHZ
The graph-theoretical thickness (shortly thickness)of graph G, denoted by Φ(G), is the minimum number of planar subgraphs into which the graph can be decomposed, and a graph that can be drawn in the plane without any of its edges intersecting is called a planar graph. determining the thickness of a given graph is known to be an NP-complete problem. In this paper we introduce an application heuristic algorithm for determining the thickness. Our algorithm is based on simulated annealing optimization scheme which provide the results of the New-thick (1). We show that the simulated annealing is a efficient method to obtain good approximation for the thickness when the number vertices are at most 30 otherwise it is slower. Finally, we apply this algorithm on the heuristic algorithm Newthick and we show that the algorithm produces a good approximation and optimization solution for the thickness, and we program this algorithm with C++, and running it by laptop has RAM 2GB and CPU 2.27GHZ.
References used
BONDY, J and MURTY, U. S 2008-Graph Theory . Springer
artrand,G 1993-Applied and Algorithmic Graph Theory. McGraw-Hill,Inc, International Edition United States of America, 395
Daniel Liang,Y 2010-Introduction to Programming With C++. Pearson Education International, second edition United States of America, 694
Eles, P 2010- Simulated Annealing.Department of Computer and Information Science (IDA)Linköpings Universitet
JOHN,M. MICHAEL,J and JEFFRY,L 2008-Combinatorics and Graph Theory, second edition Springer, 392
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