M.S. Theses

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Browsing M.S. Theses by Author "Altok, Serdar."

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    Convexity in graphs
    (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2011., 2011.) Erey, Aysel.; Ekim Aşıcı, Tınaz.; Altok, Serdar.
    The idea of finding analogies and generalizations to some concepts from continuous mathematics has led to the study of several new topics in discrete structures. Convexity is such a concept that has been widely studied in graphs during the last few decades. In this thesis, we focus on the notions of geodetic and hull sets. First, in Chapter 2, we survey a number of results concerning these two notions. In Chapter 3, we mainly deal with the computation of geodetic number in some special graph classes.
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    Space filling curve heuristic and the traveling salesman problem
    (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.) Charyyev, Polat.; Altok, Serdar.
    Let LSFC n denote the length of the path connecting n random points uniformly distributed over the unit square obtained by the space lling curve heuristic. For a Hilbert type of space lling curve such as; Peano, Moore, Sierpinski and Polya, we prove that for some number K, we have, for all ... ; where K depends only on the space ling curve. This thesis is motivated by the work of Gao and Steele [1], where they found an almost Gaussian tail bound for a broad class of space lling curves. By adapting the method of Rhee and Talagrand [2], we have obtained an exact Gaussian tail bound for the length of the path obtained by the space lling curve..