8143891
Different bounds on the different Betti numbers of semi-algebraic sets
A classic result in real algebraic geometry due to Oleinik-Petrovsky, Thom and Milnor, bounds the {\em topological complexity} (the sum of the Betti numbers) of basic semi-algebraic sets. This bound is tight as one can construct examples having that many connected components. However, till now no significantly better bounds were known on the individual higher Betti numbers.
In this paper we prove separate bounds on the different Betti numbers of basic semi-algebraic sets, as well as arrangements of algebraic hypersurfaces. These are the first results in this direction.
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.
75418
Combinatorial complexity in O-minimal geometry
In this paper we prove tight bounds on the combinatorial and topological complexity of sets dened in terms of n denable sets belonging to some fixed denable family of sets in an o-minimal structure. This generalizes the combinatorial parts of similar bounds known in the case of semi-algebraic and semi-Pfaffian sets, and as a result vastly increases the applicability of results on combinatorial and topological complexity of arrangements studied in discrete and computational geometry. As a sample application, we extend a Ramsey-type theorem due to Alon et al. [3], originally proved for semi-algebraic sets of fixed description complexity to this more general setting.
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.
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. >
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/).
7011829
QoS aware job scheduling in a cluster-based Web server for multimedia applications
We propose a cluster-based Web server where a few computing nodes are separately reserved for high-performance computing applications, such as multimedia, SSL, and CGI. As an example application, we consider a multimedia server that dynamically generates video units to satisfy the bit rate and bandwidth requirements of a variety of clients. To perform QoS aware scheduling of multiple multimedia jobs on the computing servers, a two-step algorithm is proposed. The first step is to fairly schedule multimedia streams to satisfy each stream's QoS requirement; and the second step is to balance the workload among heterogeneous computing nodes in the cluster. We propose a new quota-based adaptive coscheduling (QACS) algorithm that greatly reduces delay jitter by eliminating the out-of-order departure for outgoing streams, as well as achieves high throughput in a heterogeneous cluster. Experimental results show that the proposed scheduling technique gives adequate QoS guarantees to multiple streams.
2511594
Specification Synthesis for Monitoring and Analysis of MANET Protocols
This paper introduces an approach to automatic synthesis of the specification models of routing protocol behavior from the observed flow of the network traffic. In particular, our technique generalizes the monitored sequences of routing messages constructing a high-level abstract view of the protocol. The basis of our method is similar to inductive logic programming technique that derives a sound hypothesis from the individual examples. The preliminary experiments are presented on the example of AODV ad-hoc routing protocol.
43271530
Compositional analysis for verification of parameterized systems
Many safety-critical systems that have been considered by the verification community are parameterized by the number of concurrent components in the system, and hence describe an infinite family of systems. Traditional model checking techniques can only be used to verify specific instances of this family. In this paper, we present a technique based on compositional model checking and program analysis for automatic verification of infinite families of systems. The technique views a parameterized system as an expression in a process algebra (CCS) and interprets this expression over a domain of formulas (modal mu-calculus), considering a process as a property transformer. The transformers are constructed using partial model checking techniques. At its core, our technique solves the verification problem by finding the limit of a chain of formulas. We present a widening operation to find such a limit for properties expressible in a subset of modal mu-calculus. We describe the verification of a number of parameterized systems using our technique to demonstrate its utility.
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)
12323199
On Context-Specific Substitutability of Web Services
Web service substitution refers to the problem of identifying a service that can replace another service in the context of a composition with a specified functionality. Existing solutions to this problem rely on detecting the functional and behavioral equivalence of a particular service to be replaced and candidate services that could replace it. We introduce the notion of context-specific substitutability, where context refers to the overall functionality of the composition that is required to be maintained after replacement of its constituents. Using the context information, we investigate two variants of the substitution problem, namely environment-independent and environment- dependent, where environment refers to the constituents of a composition and show how the substitutability criteria can be relaxed within this model. We provide a logical formulation of the resulting criteria based on model checking techniques as well as prove the soundness and completeness of the proposed approach.