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The traveling salesman problem is although looking very simple problem but it is an important combinatorial problem. In this thesis I have tried to find the shortest distance tour in which each city is visited exactly one time and return to the starting city. I have tried to solve traveling salesman problem using multilevel graph partitioning approach.Although traveling salesman problem itself very difficult as this problem is belong to the NP-Complete problems but I have tried my best to solve this problem using multilevel graph partitioning it also belong to the NP-Complete problems. I have solved this thesis by using the k-mean partitioning algorithm which divides the problem into multiple partitions and solving each partition separately and its solution is used to improve the overall tour by applying Lin Kernighan algorithm on it. Through all this I got optimal solution which proofs that solving traveling salesman problem through graph partition scheme is good for this NP-Problem and through this we can solved this intractable problem within few minutes.Keywords: Graph Partitioning Scheme, Traveling Salesman Problem.

archives@tulane.edu / Although interspecific competition and relevant coexistence mechanisms are core concepts in ecology and evolution, most such research has focused on two-species interactions. Lacking is important information on how and when interspecific competition operates in more complex species assemblages. This dissertation examined interspecific competition and coexistence mechanisms between a focal species, the American redstart (Setophaga ruticilla, Parulidae) and its potential competitors in multiple communities. Using a theoretical framework that builds on the well documented population ecology of redstarts, combined with interspecific dietary overlaps, I demonstrate ongoing interspecific competition. I found that species generally both overlap highly in diet and exhibit small, but consistent, differences consistent with their foraging behavioral differences. Although some competitive interactions were mediated by direct aggressive interactions, this research also highlighted diffuse competition as more important than previously recognized. My findings also differed from systems that have shown similar patterns insofar as high dietary overlaps persisted during times of resource scarcity, were driven by overlaps on low value prey taxa, and did not involve exclusive use of any resources by different competitors. All of these factors increase the potential negative demographic effects of interspecific competition, some of which have been documented in these bird species. A long history of competition studies in these warblers has shown large differences in foraging behavior among species, assumed to be what allows coexistence. However, it is not clear how and if differences in foraging behavior correspond to differences in resource use. I confirmed that locally coexisting study species differed almost completely in foraging behavior, particularly in microhabitat use. Likewise, using a variety of arthropod sampling methods, I found that microhabitats differed greatly in their available prey. Combining the large differences in foraging behavior with available prey significantly predicted the small dietary differences, although it did a poor job of explaining the already limited variation in diet. Overall, I found mixed support for behavioral niche partitioning, leading me to examine alternative mechanisms of coexistence. Contrary to past work focused on interspecific interactions, I found that population level forces dominate in determining local distributions, with birds of the same species being more evenly distributed due to intraspecific territoriality. This pattern led to higher local (point count scale) species richness, and greater community covariance than predicted. This intraspecific territoriality and repulsion is proposed as as a novel coexistence mechanism. / 1 / Cody M. Kent

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