The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...

This thesis broadly focuses on the design and analysis of algorithmic tools leading to approximation algorithms with provably good performance guarantees. We were especially interested in problems that have highly practical importance yet possess a fundamental structure, such as integer covering, network design, graph partitioning, and discrete location problems. In particular, our main contrib...

the facet of knapsack ploytope, i.e. convex hull of 0-1 points satisfying a given linear inequality has been presented in this current paper. such type of facets plays an important role in set covering set partitioning, matroidal-intersection vertex- packing, generalized assignment and other combinatorial problems. strong covers for facets of knapsack ploytope has been developed in the first pa...

We propose a data-mining approach that produces generalized query patterns (with generalized keywords) from the raw user logs of the Microsoft Encarta search engine (http://encarta.msn.com). Those query patterns can act as cache of the search engine, improving its performance. The cache of the generalized query patterns is more advantageous than the cache of the most frequent user queries since...

This paper is intended to give a concise understanding of the facial structure of previously separately investigated polyhedra. It introduces the notion of transitive packing and the transitive packing polytope and gives cutting plane proofs for huge classes of valid inequalities of this polytope. We introduce generalized cycle, generalized clique, generalized antihole, generalized antiweb, gen...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

We give examples of closed hyperbolic 3-manifolds with first Betti number 2 and 3 for which no sequence of finite abelian covering spaces increases the first Betti number. For 3-manifolds M with first Betti number 2 we give a characterization in terms of some generalized self-linking numbers of M , for there to exist a family of Zn covering spaces, Mn, in which β1(Mn) increases linearly with n....

We investigate conditions on a computable metric space under which each co-computably enumerable set satisfying certain topological properties must be computable. We examine the notion of local computability and show that the result by which in a computable metric space which has the effective covering property and compact closed balls each co-c.e. circularly chainable continuum which is not ch...

We give examples of closed hyperbolic 3-manifolds with first Betti number 2 and 3 for which no sequence of finite abelian covering spaces increases the first Betti number. For 3-manifolds M with first Betti number 2 we give a characterization in terms of some generalized self-linking numbers of M , for there to exist a family of Zn covering spaces, Mn, in which β1(Mn) increases linearly with n....