19,472 research outputs found
NETEMBED: A Network Resource Mapping Service for Distributed Applications
Emerging configurable infrastructures such as large-scale overlays and grids, distributed testbeds, and sensor networks comprise diverse sets of available computing resources (e.g., CPU and OS capabilities and memory constraints) and network conditions (e.g., link delay, bandwidth, loss rate, and jitter) whose characteristics are both complex and time-varying. At the same time, distributed applications to be deployed on these infrastructures exhibit increasingly complex constraints and requirements on resources they wish to utilize. Examples include selecting nodes and links to schedule an overlay multicast file transfer across the Grid, or embedding a network experiment with specific resource constraints in a distributed testbed such as PlanetLab. Thus, a common problem facing the efficient deployment of distributed applications on these infrastructures is that of "mapping" application-level requirements onto the network in such a manner that the requirements of the application are realized, assuming that the underlying characteristics of the network are known. We refer to this problem as the network embedding problem. In this paper, we propose a new approach to tackle this combinatorially-hard problem. Thanks to a number of heuristics, our approach greatly improves performance and scalability over previously existing techniques. It does so by pruning large portions of the search space without overlooking any valid embedding. We present a construction that allows a compact representation of candidate embeddings, which is maintained by carefully controlling the order via which candidate mappings are inserted and invalid mappings are removed. We present an implementation of our proposed technique, which we call NETEMBED – a service that identify feasible mappings of a virtual network configuration (the query network) to an existing real infrastructure or testbed (the hosting network). We present results of extensive performance evaluation experiments of NETEMBED using several combinations of real and synthetic network topologies. Our results show that our NETEMBED service is quite effective in identifying one (or all) possible embeddings for quite sizable queries and hosting networks – much larger than what any of the existing techniques or services are able to handle.National Science Foundation (CNS Cybertrust 0524477, NSF CNS NeTS 0520166, NSF CNS ITR 0205294, EIA RI 0202067
Continuous selections of multivalued mappings
This survey covers in our opinion the most important results in the theory of
continuous selections of multivalued mappings (approximately) from 2002 through
2012. It extends and continues our previous such survey which appeared in
Recent Progress in General Topology, II, which was published in 2002. In
comparison, our present survey considers more restricted and specific areas of
mathematics. Note that we do not consider the theory of selectors (i.e.
continuous choices of elements from subsets of topological spaces) since this
topics is covered by another survey in this volume
Extending Whitney's extension theorem: nonlinear function spaces
We consider a global, nonlinear version of the Whitney extension problem for
manifold-valued smooth functions on closed domains , with non-smooth
boundary, in possibly non-compact manifolds. Assuming is a submanifold with
corners, or is compact and locally convex with rough boundary, we prove that
the restriction map from everywhere-defined functions is a submersion of
locally convex manifolds and so admits local linear splittings on charts. This
is achieved by considering the corresponding restriction map for locally convex
spaces of compactly-supported sections of vector bundles, allowing the even
more general case where only has mild restrictions on inward and outward
cusps, and proving the existence of an extension operator.Comment: 37 pages, 1 colour figure. v2 small edits, correction to Definition
A.3, which makes no impact on proofs or results. Version submitted for
publication. v3 small changes in response to referee comments, title
extended. v4 crucial gap filled, results not affected. v5 final version to
appear in Annales de l'Institut Fourie
The existence of an inverse limit of inverse system of measure spaces - a purely measurable case
The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov
[10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given
Connectedness modulo a topological property
Let be a topological property. We say that a space is
-connected if there exists no pair and of disjoint
cozero-sets of with non- closure such that the remainder
is contained in a cozero-set of with
closure. If is taken to be "being empty" then -connectedness coincides with connectedness in its usual sense. We
characterize completely regular -connected spaces, with
subject to some mild requirements. Then, we study conditions
under which unions of -connected subspaces of a space are
-connected. Also, we study classes of mappings which preserve
-connectedness. We conclude with a detailed study of the special
case in which is pseudocompactness. In particular, when
is pseudocompactness, we prove that a completely regular space
is -connected if and only if is connected, and that -connectedness is
preserved under perfect open continuous surjections. We leave some problems
open.Comment: 12 page
Every hierarchy of beliefs is a type
When modeling game situations of incomplete information one usually considers
the players' hierarchies of beliefs, a source of all sorts of complications.
Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program"
is that hierarchies of beliefs can be replaced by "types". The types constitute
the "type space". In the purely measurable framework Heifetz and Samet (1998)
formalize the concept of type spaces and prove the existence and the uniqueness
of a universal type space. Meier (2001) shows that the purely measurable
universal type space is complete, i.e., it is a consistent object. With the aim
of adding the finishing touch to these results, we will prove in this paper
that in the purely measurable framework every hierarchy of beliefs can be
represented by a unique element of the complete universal type space.Comment: 19 page
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