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.
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. >
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.
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.
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.
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.
2815801
Architecture for resource allocation services supporting interactive remote desktop sessions in utility grids
Emerging large scale utility computing systems like Grids promise computing and storage to be provided to end users as a utility. System management services deployed in the middleware are a key to enabling this vision. Utility Grids provide a challenge in terms of scale, dynamism, and heterogeneity of resources and workloads. In this paper, we present a model based architecture for resource allocation services for Utility Grids. The proposed service is built in the context of interactive remote desktop session workloads and takes application performance QoS models into consideration. The key design guidelines are hierarchical request structure, application performance models, remote desktop session performance models, site admission control, multi-variable resource assignment system, and runtime session admission control. We have also built a simulation toolkit that can handle mixed batch and remote desktop session requests, and have implemented our proposed resource allocation service into the toolkit. We present some results from experiments done using the toolkit. Our proposed architecture for resource allocation services addresses the needs of emerging utility computing systems and captures the key concepts and guidelines for building such services in these environments.
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.
2629561
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.
17954434
Fast proxy delivery of multiple streaming sessions in shared running buffers
With the falling price of memory, an increasing number of multimedia servers and proxies are now equipped with a large memory space. Caching media objects in the memory of a proxy helps to reduce the network traffic, the disk I/O bandwidth requirement, and the data delivery latency. The running buffer approach and its alternatives are representative techniques to caching streaming data in the memory. 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 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 in the proxy to address these limits. Considering user access patterns and characteristics of the requested media objects, our techniques adaptively 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 achieve significant performance improvement by effectively using the shared running buffers.