Relation between „3 Utility Problem‟ And „Eulerian Trail‟
Journal Title: IOSR Journals (IOSR Journal of Computer Engineering) - Year 2014, Vol 16, Issue 2
Abstract
Abstract: There are two most renowned puzzles whose algorithms have been developed in the computer science (field- Algorithms and design Analysis) that are impossible to solve till date. They are 3 utility problem and Eulerian trail. Both of them have some methods and have to be done according to some rule. A lot of work has been done to find why this happens and what application can be drawn out of it. The answer is though simple, these problems cannot be solved in 2- dimension and we need a 3-dimensional environment to solve them. But hardly anyone have ever thought that Eulerian theorem is not a new thing but a result of 3 utility problem, means if 3 utility problem exists then Eulerian puzzle too. Actually both puzzles are invented in different time but are related to one other, though their methods may be different. This paper will prove that why some figure are Eulerian Trial and other not. It will give result that if we don‟t follow rules of 3 utility problem then we cannot make any Eulerian Trail. The paper gives six conditions/ rules and two theorems that will help in making Algorithms for finding relation between these two puzzles. Means by following these rules one can make Algorithm easily for showing relation between two puzzles as shown in „Explanation by an example‟ section. Both the problems are giving same result that is we need a 3-dimensional environment. So there must be something that creates a path in between these two problems. Moreover this research work will give answers of some other questions like – Why Eulerian trial occur when there are 3 or more than 3 internal figures exists in any figure with odd number of edges?
Authors and Affiliations
Yashasvini Sharma
Keywords
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