The Hardness of Finding Linear Ranking Functions for Lasso Programs

Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem is known to be in coNP when variables range over the integers and in PTIME for the rational numbers, or real numbers. Here we show that deciding whether a linear-constraint loop with a precondition, specifically with partially-specified input, has a linear ranking function is EXPSPACE-hard over the integers, and PSPACE-hard over the rationals. The precise complexity of these decision problems is yet unknown. The EXPSPACE lower bound is derived from the reachability problem for Petri nets (equivalently, Vector Addition Systems), and possibly indicates an even stronger lower bound (subject to open problems in VAS theory). The lower bound for the rationals follows from a novel simulation of Boolean programs. Lower bounds are also given for the problem of deciding if a linear ranking-function supported by a particular form of inductive invariant exists. For loops over integers, the problem is PSPACE-hard for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State Systems", for the opportunity to present an early draft of this wor

Index ordering by query-independent measures

Conventional approaches to information retrieval search through all applicable entries in an inverted file for a particular collection in order to find those documents with the highest scores. For particularly large collections this may be extremely time consuming. A solution to this problem is to only search a limited amount of the collection at query-time, in order to speed up the retrieval process. In doing this we can also limit the loss in retrieval efficacy (in terms of accuracy of results). The way we achieve this is to firstly identify the most “important” documents within the collection, and sort documents within inverted file lists in order of this “importance”. In this way we limit the amount of information to be searched at query time by eliminating documents of lesser importance, which not only makes the search more efficient, but also limits loss in retrieval accuracy. Our experiments, carried out on the TREC Terabyte collection, report significant savings, in terms of number of postings examined, without significant loss of effectiveness when based on several measures of importance used in isolation, and in combination. Our results point to several ways in which the computation cost of searching large collections of documents can be significantly reduced

Dublin City University at the TREC 2006 terabyte track

For the 2006 Terabyte track in TREC, Dublin City University’s participation was focussed on the ad hoc search task. As per the pervious two years [7, 4], our experiments on the Terabyte track have concentrated on the evaluation of a sorted inverted index, the aim of which is to sort the postings within each posting list in such a way, that allows only a limited number of postings to be processed from each list, while at the same time minimising the loss of effectiveness in terms of query precision. This is done using the Físréal search system, developed at Dublin City University [4, 8]

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

Top subset retrieval on large collections using sorted indices

In this poster we describe alternative inverted index structures that reduce the time required to process queries, produce a higher query throughput and still return high quality results to the end user. We give results based upon the TREC Terabyte dataset showing improvements that these indices give in terms of effectiveness and efficiency

Optimization strategy for actuator and sensor placement in active structural acoustic control

In active structural acoustic control the goal is to reduce the sound radiation of a structure by means of changing the vibrational behaviour of that structure. The performance of such an active control system is to a large extent determined by the locations of the actuators and sensors. In this work an approach is presented for the optimization of the actuator and sensor locations. The approach combines a numerical modelling technique, for predicting the control performance, and genetic optimization, to find the optimal actuator and sensor locations. The approach is tested for a setup consisting of clamped rectangular plate with a piezoelectric actuator and either structural or acoustic sensors. The results show that a control system with optimal actuator and sensor configuration outperforms an arbitrary chosen configuration in terms of reduction in radiated sound power