Analyzing the worst-case complexity of the k-level in a planar arrangement of n curves is a fundamental problem in combinatorial geometry. We give the first subquadratic upper bound (roughly O(nk1 2=3s)) for curves that are graphs of polynomial functions of an arbitrary fixed degree s. Previously, nontrivial results were known only for the case s = 1 and s = 2. We also improve the earlier bound...

In this paper we present TransUCP, a general framework for transformational analogy. Using our framework we demonstrate that transformational analogy does not meet a crucial condition for a well-known worst-case complexity scenario, and therefore the results about plan adaptation being computationally harder than planning from the scratch does not apply to transformational analogy. We prove thi...

Tools for worst-case execution time (WCET) analysis request several code annotations from the user. However, most of them could be avoided or being annotated more comfortably if the compilers would support WCET analysis. This paper provides a clear categorization of code annotations for WCET analysis and discusses the positive impact on code annotations a compiler-support on WCET analysis would...

The presence of infeasible paths in a program is a source of imprecision in the Worst-Case Execution Time (WCET) analysis. Detecting, expressing and exploiting such paths can improve the WCET estimation or, at least, improve the confidence we have in estimation precision. In this article, we propose an extension of the FFX format to express conflicts over paths and we detail two ways of enhanci...

The fully-functional succinct tree representation of Navarro and Sadakane (ACM Transactions on Algorithms, 2014) supports a large number of operations in constant time using 2n + o(n) bits. However, the full idea is hard to implement. Only a simplified version with O(lg n) operation time has been implemented and shown to be practical and competitive. We describe a new variant of the original id...

The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from n logn to n, if the entropy of the ...

We propose a novel consequence-based algorithm for TBox reasoning in SHIQ. This work is at very early stage: we have no experimental results and we have not even proved completeness. Instead, we focus on explaining the intuitions behind the algorithm, and show that it has all the favorable properties of existing consequence-based algorithms, namely optimal worst-case complexity, one-pass classi...

This short note considers and resolves the apparent contradiction between known worst-case complexity results for first and second-order methods for solving unconstrained smooth nonconvex optimization problems and a recent note by Jarre (2011) implying a very large lower bound on the number of iterations required to reach the solution’s neighbourhood for a specific problem with variable dimension.

We address the problem of computing accurate Worst-Case Execution Time (WCET) on pipelined architectures with caches. We propose a fully automatic and modular methodology based on program slicing and real-time modelchecking. We have implemented our methodology and applied it to standard benchmarks. To further validate the approach, we also compare our results to the real execution times of the ...

This paper is motivated through the advantages offered by employing real-time (priority-driven) scheduling (RTS) for efficiently implementing quality-of-service guarantees. For employing RTS (e.g. for conferencing), a-priori knowledge about worst-case execution times (WCET) of the decoding process is required. With our new approach (focussing of MPEG 2 with variable bitrates) the resource usage...