http://hdl.handle.net/2092/194 Publications and research submitted by the faculty members of the Department of Mathematics and Computer Science. Sat, 25 May 2013 23:45:05 GMT 2013-05-25T23:45:05Z http://hdl.handle.net/2092/409 "Hierarchical routing in sensor networks using κ-dominating sets " Rieck, Michael Q.; Dhar, Subhankar For a connected graph, representing a sensor network, distributed algorithms for the Set Covering Problem can be employed to construct reasonably small subsets of the nodes, called k-SPR sets. Such a set can serve as a virtual backbone to facilitate shortest path routing, as introduced in [4] and [14]. When employed in a hierarchical fashion, together with a hybrid (partly proactive, partly reactive) strategy, the κ-SPR set methods become highly scalable, resulting in guaranteed minimal path routing, with comparatively little overhead. © Springer-Verlag Berlin Heidelberg 2005. Michael Q. Rieck is Associate Professor of Computer Science in the Department of Math and Computer Science at Drake University. He can be contacted at michael.rieck@drake.edu Sat, 01 Jan 2005 00:00:00 GMT http://hdl.handle.net/2092/409 2005-01-01T00:00:00Z http://hdl.handle.net/2092/261 "Distributed routing algorithms for multi-hop ad hoc networks using d-hop connected d-dominating sets" Rieck, Michael Q.; Pai, Sukesh; Dhar, Subhankar This paper describes a distributed algorithm (generalized d-CDS) for producing a variety of d-dominating sets of nodes that can be used to form the backbone of an ad hoc wireless network. In special cases (ordinary d-CDS), these sets are also d-hop connected and has a desirable “shortest path property”. Routing via the backbone created is also discussed. The algorithm has a “constant time” complexity in the limited sense that it is unaffected by expanding the size of the network as long as the maximal node degree is not allowed to increase too. The performances of this algorithm for various parameters are compared, and also compared with other algorithms. Michael Q. Rieck is Assistant Professor of Computer Science in the Department of Math and Computer Science at Drake University. Fri, 22 Apr 2005 00:00:00 GMT http://hdl.handle.net/2092/261 2005-04-22T00:00:00Z http://hdl.handle.net/2092/241 "On the Taketa bound for normally monomial p-groups of maximal class" Keller, Thomas Michael; Ragan, Dustin; Tims, Geoffrey T. A longstanding problem in the representation theory of finite solvable groups, sometimes called the Taketa problem, is to find strong bounds for the derived length dl(G) in terms of the number |cd(G)| of irreducible character degrees of the group G. For p-groups an old result of Taketa implies that dl(G)|cd(G)|, and while it is conjectured that the true bound is much smaller (in fact, logarithmic) for large dl(G), it turns out to be extremely difficult to improve on Taketa's bound at all. Here, therefore, we suggest to first study the problem for a restricted class of p-groups, namely normally monomial p-groups of maximal class. We exhibit some structural features of these groups and show that if G is such a group, then . Geoffrey T. Tims is a 2003 graduate of the Department of Mathematics and Computer Science, Drake University. Thu, 15 Jul 2004 00:00:00 GMT http://hdl.handle.net/2092/241 2004-07-15T00:00:00Z http://hdl.handle.net/2092/240 "Inertia of the stein transformation with respect to some nonderogatory matrices" DeAlba, Luz M. Let A be an n-by-n nonderogatory matrix all of whose eigenvalues lie on the unit circle, and let and be nonnegative integers with + = n. Let ′ and ′ be positive integers and ′ a nonnegative integer with ′ + ′ + ′ = n. In this paper we explore the existence of a Hermitian nonsingular matrix K with inertia ( , , 0), such that the Stein transformation of K corresponding to A, SA(K) = K − AKA*, is a Hermitian matrix with inertia ( ′, ′, ′). The study is done by reducing A to Jordan canonical form. If C is an n-by-n nonderogatory matrix all of whose eigenvalues lie on the imaginary axis, then the results obtained for SA(K) are valid for the Lyapunov transformation, LC(K) = CK + KC*, of K corresponding to C. Proceedings of the Fourth Conference of the International Linear Algebra Society. Mon, 01 Jul 1996 00:00:00 GMT http://hdl.handle.net/2092/240 1996-07-01T00:00:00Z