6997851
Computing the betti numbers of arrangements
(MATH) In this paper, we consider the problem of computing the Betti numbers of an arrangement of $n$ compact semi-algebraic sets, $S_1,\ldots,S_n \subset \R^k$, where each $S_i$ 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 $\ell$-th Betti number, $\beta_\ell(\cup_i S_i), 0 \leq \ell \leq k-1$, using $O(n^{\ell+2})$ algebraic operations. Additionally, one has to perform linear algebra on matrices of size bounded by $O(n^{\ell+1})$. All previous algorithms for computing the Betti numbers of arrangements, triangulated the arrangement giving rise to a complex of size $O(n^{2^k})$ in the worst case. To our knowledge this is the first algorithm for computing $\beta_\ell(\cup_i S_i)$ that does not rely on such a global triangulation, and has a graded complexity which depends on $\ell$.
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/).
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.
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. >
13887054
A resource management framework for interactive Grids
Traditional use of Grid computing systems has been for batch jobs in the scientific and academic computing. We envision the next generation Grid computing systems to support graphical interactive sessions. In this paper, we propose a resource management framework for supporting graphical interactive sessions in a Grid computing system. We describe the high-level architectural resource management framework distributed among the submission node, central scheduler node, and the execution node. We then describe in detail the resource management framework on the execution node. The description of the resource management framework on the scheduler node is kept at a high level in this paper. The framework on execution nodes consists of Resource Management Agents, an Admission Control system and Application Predictor system. The agents on the execution node are Startup Agents, Sensor Agents, Monitoring Agents, Aggregator Agents, Enforcement Agents and Registration Agents. The Session Admission Control system is responsible for determining if a new application session can be admitted to the execution node. An Application Predictor system is responsible for predicting the resource utilization behavior of applications based on data obtained from the Resource Management Agents. The proposed framework allows for implementation of a scalable and extensible middleware for interactive Grid resource management. It supports fine-grained performance guarantees specified in service level agreements and brings forth some important and novel contributions to enable graphical interactive sessions on Grids. Copyright © 2004 John Wiley & Sons, Ltd.
8225775
A global lower bound on parameter estimation error with periodic distortion functions
We present a global Ziv-Zakai (1969) type lower bound on the mean square error for estimation of signal parameter vectors, where some components of the distortion function may be periodic. Periodic distortion functions arise naturally in the context of direction of arrival or phase estimation problems. The bound is applied to an image registration problem, and compared to the performance of the maximum-likelihood estimator (MLE).
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.
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.
2153688
Architecture and Environment for Enabling Interactive Grids
Traditional use of grid computing allows a user to submit batch jobs in a grid environment. We believe, next generation grids will extend the application domain to include interactive graphical sessions. We term such grids Interactive Grids. In this paper, we describe some of the challenges involved in building Interactive Grids. These include fine grain access control, performance QoS guarantees, dynamic account management, scheduling, and user data management. We present the key architectural concepts in building Interactive Grids viz. hierarchical sessions, hierarchical admission control, hierarchical agents, classes of dynamic accounts, application profiling, user data management, scheduling for interactive sessions, persistent environment settings, and exporting remote desktop. We also describe IGENV, an environment for enabling interactive grids. IGENV consists of GISH –‘Grid Interactive Shell’, Controlled Desktop, SAC –‘Session Admission Control’ module, GMMA –‘Grid Monitoring and Management Agents’, and Policy Engine. We also present our testbed implementation for Interactive Grids using and extending Globus Toolkit 2.0 for the Grid middleware infrastructure, and VNC as the remote display technology.