5085726
Uniform quantifier elimination and constraint query processing
Saugata Basu* Mathematical Sciences Research Institute Berkeley, CA 94720, USA
8618090
Computing the first Betti number and the connected components of semi-algebraic sets
In this paper we describe the first singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. We also describe algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one.
33624885
On the combinatorial and topological complexity of a single cell
The problem of bounding the combinatorial complexity of a single connected component (a single cell) of the complement of a set of a geometric objects in R/sup k/, each object of constant description complexity, is an important problem in computational geometry which has attracted much attention over the past decade. It has been conjectured that the combinatorial complexity of a single cell is bounded by a function much closer to O(n/sup k-1/) rather than O(n/sup k/) which is the bound for the combinatorial complexity of the whole arrangement. Till now, this was known to be rule only for k/spl les/3 and only for some special cases in higher dimensions. A classic result in real algebraic geometry due to Oleinik-Petrovsky, Thom and Milnor, bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. However, till now no better bounds were known if we restricted attention to a single connected component of a basic semi-algebraic set. In this paper, we show how these two problems are related. We prove a new bound on the sum of the Betti numbers of one connected component of a basic semi-algebraic set which is an improvement over the Oleinik-Petrovsky-Thom-Milnor bound. This also implies that the topological complexity of a single cell, measured by the sum of the Betti numbers, is bounded by O(n/sup k-1/).
32812813
Design of CAECC-Cellular Automata Based Error Correcting Code
A new scheme for designing error detecting and error correcting codes around cellular automata (CA) is reported. A simple and efficient scheme for generating SEC-DED codes is presented which can also be extended for generating codes with higher distances. A CA-based hardware scheme for very fast decoding (and correcting) of the codewords is also reported. >
24764914
Computing the Betti numbers of arrangements via spectral sequences
In this paper, we consider the problem of computing the Betti numbers of an arrangement of n compact semi-algebraic sets, S1,...,Sn ⊂ Rk, where each Si is described using a constant number of polynomials with degrees bounded by a constant. Such arrangements are ubiquitous in computational geometry. We give an algorithm for computing lth Betti number, β(∪i=1n Si), 0 ≤ l ≤ k - 1 using O(nl+2) algebraic operations. Additionally, one has to perform linear algebra on integer matrices of size bounded by O(nl+2). All previous algorithms for computing the Betti numbers of arrangements, triangulated the whole arrangement giving rise to a complex of size O(n2k) in the worst case. Thus, the complexity of computing the Betti numbers (other than the zeroth one) for these algorithms was O(n2k). To our knowledge this is the first algorithm for computing βl(∪i=1n Si) that does not rely on such a global triangulation, and has a graded complexity which depends on l.
18808745
An improved algorithm for quantifier elimination over real closed fields
We give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms the combinatorial part of the complexity of this new algorithm is independent of the number of free variables. Moreover, under the assumption that each polynomial in the input depend only on a constant number of the free variables, the algebraic part of the complexity can also be made independent of the number of free variables. This new feature of our algorithm allows us to obtain a new algorithm for a variant of the quantifier elimination problem. We give an almost optimal algorithm for this new problem, which we call the uniform quantifier elimination problem and apply it to solve a problem arising in the field of constraint databases. No algorithm with reasonable complexity bound was known for this latter problem till now. We also point out interesting logical consequences of this algorithmic result, concerning the expressive power of a constraint query language over the reals. Moreover, our improved algorithm for performing quantifier elimination immediately leads to improved algorithms for several problems for which quantifier elimination is a basic step, for example, the problem of computing the closure of a given semi-algebraic set.
5532229
Modeling Web Services by Iterative Reformulation of Functional and Non-functional Requirements
We propose an approach for incremental modeling of composite Web services. The technique takes into consideration both the functional and non-functional requirements of the composition. While the functional requirements are described using symbolic transition systems—transition systems augmented with state variables, function invocations, and guards; non-functional requirements are quantified using thresholds. The approach allows users to specify an abstract and possibly incomplete specification of the desired service (goal) that can be realized by selecting and composing a set of pre-existing services. In the event that such a composition is unrealizable, i.e. the composition is not functionally equivalent to the goal or the non-functional requirements are violated, our system provides the user with the causes for the failure, that can be used to appropriately reformulate the functional and/or non-functional requirements of the goal specification.
12026284
mmGrid: distributed resource management infrastructure for multimedia applications
We are developing mmGrid (Multimedia Grid) as an extensible middleware architecture supporting multimedia applications in a grid computing environment. Our vision is to provide support for interactive applications from the following domains: graphics, visualization, streaming media and tele-immersion. The initial deployment will be within an enterprise as a mechanism for provisioning computing resources. However the scheduling system of mmGrid will be flexible, and will allow interactive and batch jobs to use the grid-computing paradigm. This paper presents our argument for using remote display technology in this environment. We also report on the use cases we support at this point, the system architecture for mmGrid and our research directions.
9852130
Parallel Web Service Composition in MoSCoE: A Choreography-Based Approach
We present a goal-driven approach to model a choreographer for realizing composite Web services. In this framework, the users start with an abstract, and possibly incomplete functional specification of a desired goal service. This specification is used to compose a choreographer that allows communication between the client and the set of available component services, and is functionally equivalent to the goal service. However, if such a composition cannot be realized, the proposed approach identifies the cause(s) for the failure of composition. This information can be used by the user to minimally reformulate the goal to reduce the `gap' between the desired functionality. The process can be iterated until a feasible composition is realized or the user decides to abort. The approach ensures that (i) a choreographer, if one is produced by our composition algorithm, in fact realizes the user-specified goal functionality; and (ii) the algorithm is guaranteed to find a composition that meets the user needs as captured in the goal specifications (whenever such a composition exists)
5783178
SRB: shared running buffers in proxy to exploit memory locality of multiple streaming media sessions
With the falling price of the memory, an increasing number of multimedia servers and proxies are now equipped with a large DRAM memory space. Caching media objects in the memory of a proxy helps to reduce network traffic, disk I/O bandwidth requirement, and data delivery latency. The running buffer approach and its alternatives are representative techniques to cache streaming data in the memory. However, there are two limits in the existing techniques. First, although multiple running buffers for the same media object co-exist in a given processing period, data sharing among the multiple buffers is not considered. Second, user access patterns are not insightfully considered in the buffer management. In this paper, we propose two techniques based on shared running buffers (SRB) in the proxy to address these limits. Considering user access patterns and characteristics of the requested media objects, our techniques adoptively allocate memory buffers to fully utilize the currently buffered data of streaming sessions, with the aim to reduce both the server load and the network traffic. Experimentally comparing with several existing techniques, we show that the proposed techniques have achieved significant performance improvement by effectively using the shared running buffers.
15323130
MoSCoE: A Framework for Modeling Web Service Composition and Execution
Development of sound approaches and software tools for specification, assembly, and deployment of composite Web services from independently developed components promises to enhance collaborative software design and reuse. In this context, the proposed research introduces a new incremental approach to service composition, MoSCoE (Modeling Web Service Composition and Execution), based on the three steps of abstraction, composition and refinement. Abstraction refers to the high-level description of the service desired (goal) by the user, which drives the identification of an appropriate composition strategy. In the event that such a composition is not realizable, MoSCoE guides the user through successive refinements of the specification towards a realizable goal service that meets the user requirements.