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.
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/).
10508326
The Combinatorial and Topological Complexity of a Single Cell 


Abstract. The problem of bounding the combinatorial complexity of a single connected component (a single cell) of the complement of a set of n geometric objects in Rk, 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(nk-1) rather than O(nk) which is the bound for the combinatorial complexity of the whole arrangement. Until now, this was known to be true only for k ≤ 3 and only for some special cases in higher dimensions. A classic result in real algebraic geometry due to Oleinik and Petrovsky [15], Thom [18], and Milnor [14], bounds the topological complexity (the sum of the Betti numbers) of basic semi-algebraic sets. However, until 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(nk-1) . The techniques used for proving this topological result combined with those developed by Halperin and Sharir for the single cell problem in three dimensions allow us to prove a bound of O(nk-1+ε) on the combinatorial complexity of a single cell. Finally, we show that under a certain natural geometric assumption on the objects (namely, that whenever they intersect, the intersection is robustly transversal) it is possible to prove a bound of O(nk-1) on the combinatorial complexity of a single cell. 

9536962
On the combinatorial and algebraic complexity of quantifier elimination
In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this data. A new feature of this algorithm is that the role of the algebraic part (the dependence on the degrees of the imput polynomials) and the combinatorial part (the dependence on the number of polynomials) are sparated. Another new feature is that the degrees of the polynomials in the equivalent quantifier-free formula that is output, are independent of the number of input polynomials. As special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields, and also for solving the existential problem in the first order theory over real closed fields, are obtained.
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.
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.
908197
WebSob: A Tool for Robustness Testing of Web Services
Web services are a popular way of implementing a service-oriented architecture. Testing can be used to help assure both the correctness and robustness of a web service. Because manual testing is tedious, tools are needed to automate test generation and execution for web services. This paper presents WebSob, a tool for automatically generating and executing web-service requests given a service provider's Web service description language (WSDL) specification. We have applied WebSob to freely available web services and our experiences show that WebSob can be used to quickly generate and execute web-service requests that may reveal robustness problems with no knowledge of the underlying web service implementation.
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.
8152994
Localizing Program Errors for Cimple Debugging
We present automated techniques for the explanation of counter-examples, where a counter-example should be understood as a sequence of program statements. Our approach is based on variable dependency analysis and is applicable to programs written in Cimple, an expressive subset of the C programming language. Central to our approach is the derivation of a focus-statement sequence (FSS) from a given counter-example: a subsequence of the counter-example containing only those program statements that directly or indirectly affect the variable valuation leading to the program error behind the counter-example. We develop a ranking procedure for FSSs where FSSs of higher rank are conceptually easier to understand and correct than those of lower rank. We also analyze constraints over uninitialized variables in order to localize program errors to specific program segments; this often allows the user to subsequently take appropriate debugging measures. We have implemented our techniques in the FocusCheck model checker, which efficiently checks for assertion violations in Cimple programs on a per-procedure basis. The practical utility of our approach is illustrated by its successful application to a fast, linear-time median identification algorithm commonly used in statistical analysis and in the Resolution Advisory module of the Traffic Collision Avoidance System.
37245904
Model checking the Java meta-locking algorithm
We apply the XMC model checker to the Java meta-locking algorithm, a highly optimized technique for ensuring mutually exclusive access by threads to object monitor queues. Our abstract specification of the meta-locking algorithm is fully parameterized, both on M, the number of threads, and N, the number of objects. Using XMC, we show that for a variety of values of M and N, the algorithm indeed provides mutual exclusion and freedom from lockout.
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.