Bounds on series-parallel slowdown

We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, such as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually increasing its makespan (execution time). The slowdown ratio describes how additional constraints affect the makespan. We disprove an existing conjecture positing a bound of two on the slowdown when workload is not considered. Where workload is known, we conjecture that 4/3 slowdown is always achievable, and prove our conjecture for small networks using max-plus algebra. We analyse a polynomial-time algorithm showing that achieving 4/3 slowdown is in exp-APX. Finally, we discuss the implications of our results.Comment: 12 pages, 4 figure

Effective guessing has unlikely consequences

Funding: EPSRC Grant number EP/P015638/1.A classic result of Paul, Pippenger, Szemeredi and Trotter states that DTIME(n) ⊊ NTIME(n). The natural question then arises: could the inclusion DTIME(t (n)) ⊆ NTIME(n) hold for some superlinear time-constructible function t (n)? If such a function t (n) does exist, then there also exist effective nondeterministic guessing strategies to speed up deterministic computations. In this work, we prove limitations on the effectiveness of nondeterministic guessing to speed up deterministic computations by showing that the existence of effective nondeterministic guessing strategies would have unlikely consequences. In particular, we show that if a subpolynomial amount of nondeterministic guessing could be used to speed up deterministic computation by a polynomial factor, then P ⊊ NTIME(n). Furthermore, even achieving a logarithmic speedup at the cost of making every step nondeterministic would show that SAT ∈ NTIME(n) under appropriate encodings. Of possibly independent interest, under such encodings we also show that SAT can be decided in O(n log n) steps on a nondeterministic multitape Turing machine, improving on the well-known O(n(log n)c) bound for some constant but undetermined exponent c ≥ 1.Publisher PDFPeer reviewe

Superlinear lower bounds based on ETH

Andras Z. Salamon acknowledges support from EPSRC grants EP/P015638/1 and EP/V027182/1.We introduce techniques for proving superlinear conditional lower bounds for polynomial time problems. In particular, we show that CircuitSAT for circuits with m gates and log(m) inputs (denoted by log-CircuitSAT) is not decidable in essentially-linear time unless the exponential time hypothesis (ETH) is false and k-Clique is decidable in essentially-linear time in terms of the graph's size for all fixed k. Such conditional lower bounds have previously only been demonstrated relative to the strong exponential time hypothesis (SETH). Our results therefore offer significant progress towards proving unconditional s uperlinear time complexity lower bounds for natural problems in polynomial time.Postprin

Macroscopes: models for collective decision making

We introduce a new model of collective decision making, when a global decision needs to be made but the parties only possess partial information, and are unwilling (or unable) to first create a globalcomposite of their local views. Our macroscope model captures two key features of many real-world problems: allotment structure (how access to local information is apportioned between parties, including overlaps between the parties) and the possible presence of meta-information (what each party knows about the allotment structure of the overall problem). Using the framework of communication complexity, we formalize the efficient solution of a macroscope. We present general results about the macroscope model, and also results that abstract the essential computational operations underpinning practical applications, including in financial markets and decentralized sensor networks. We illustrate the computational problem inherent in real-world collective decision making processes using results for specific functions, involving detecting a change in state (constant and step functions), and computing statistical properties (the mean).Comment: Presented at Collective Intelligence conference, 2012 (arXiv:1204.2991), 8 page

Towards exploratory reformulation of constraint models

Funding: Ian Miguel: EPSRC grant EP/V027182/1; Christopher Stone: EPSRC grant EP/V027182/1.It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to know a priori which of a set of candidate models will perform best in practice, we envisage a system that explores the space of models through a process of reformulation from an initial model, guided by performance on a set of training instances from the problem class under consideration. We plan to situate this system in a refinement-based approach, where a user writes a constraint specification describing a problem above the level of abstraction at which many modelling decisions are made. In this position paper we set out our plan for an exploratory reformulation system, and discuss progress made so far.PostprintPeer reviewe

Classification of annotation semirings over containment of conjunctive queries

Funding: This work is supported under SOCIAM: The Theory and Practice of Social Machines, a project funded by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/J017728/1. This work was also supported by FET-Open Project FoX, grant agreement 233599; EPSRC grants EP/F028288/1, G049165 and J015377; and the Laboratory for Foundations of Computer Science.We study the problem of query containment of conjunctive queries over annotated databases. Annotations are typically attached to tuples and represent metadata, such as probability, multiplicity, comments, or provenance. It is usually assumed that annotations are drawn from a commutative semiring. Such databases pose new challenges in query optimization, since many related fundamental tasks, such as query containment, have to be reconsidered in the presence of propagation of annotations. We axiomatize several classes of semirings for each of which containment of conjunctive queries is equivalent to existence of a particular type of homomorphism. For each of these types, we also specify all semirings for which existence of a corresponding homomorphism is a sufficient (or necessary) condition for the containment. We develop new decision procedures for containment for some semirings which are not in any of these classes. This generalizes and systematizes previous approaches.PostprintPeer reviewe

Exploring instance generation for automated planning

Funding: This work is supported by EPSRC grant EP/P015638/1. Nguyen Dang is a Leverhulme Early Career Fellow.Many of the core disciplines of artificial intelligence have sets of standard benchmark problems well known and widely used by the community when developing new algorithms. Constraint programming and automated planning are examples of these areas, where the behaviour of a new algorithm is measured by how it performs on these instances. Typically the efficiency of each solving method varies not only between problems, but also between instances of the same problem. Therefore, having a diverse set of instances is crucial to be able to effectively evaluate a new solving method. Current methods for automatic generation of instances for Constraint Programming problems start with a declarative model and search for instances with some desired attributes, such as hardness or size. We first explore the difficulties of adapting this approach to generate instances starting from problem specifications written in PDDL, the de-facto standard language of the automated planning community. We then propose a new approach where the whole planning problem description is modelled using Essence, an abstract modelling language that allows expressing high-level structures without committing to a particular low level representation in PDDL.Publisher PD

LADA type diabetes, celiac diasease, cerebellar ataxia and stiff person syndrome. A rare association of autoimmune disorders.

Celiac disease--in its typical form--is a chronic immune-mediated enteropathy with typical clinical symptoms that develops against gliadin content of cereal grains, and is often associated with other autoimmune diseases. In cases of atypical manifestation classic symptoms may be absent or mild, and extra-intestinal symptoms or associated syndromes dominate clinical picture. The authors present a longitudinal follow-up of such a case. A 63-years old woman was diagnosed with epilepsy at the age of 19, and with progressive limb ataxia at the age of 36, which was initially thought to be caused by cerebellar atrophy, later probably by stiff person syndrome. At the age 59, her diabetes mellitus manifested with type 2 diabetic phenotype, but based on GAD positivity later was reclassified as type 1 diabetes. Only the last check-up discovered the celiac disease, retrospectively explaining the entire disease course and neurological symptoms. By presenting this case, the authors would like to draw attention to the fact that one should think of the possibility of celiac disease when cerebellar ataxia, progressive neurological symptoms and diabetes are present at the same time. An early diagnosis may help to delay the progression of disease and help better treatment

Instance generation via generator instances

Funding: UK EPSRC grant EP/P015638/1.Access to good benchmark instances is always desirable when developing new algorithms, new constraint models, or when comparing existing ones. Hand-written instances are of limited utility and are time-consuming to produce. A common method for generating instances is constructing special purpose programs for each class of problems. This can be better than manually producing instances, but developing such instance generators also has drawbacks. In this paper, we present a method for generating graded instances completely automatically starting from a class-level problem specification. A graded instance in our present setting is one which is neither too easy nor too difficult for a given solver. We start from an abstract problem specification written in the Essence language and provide a system to transform the problem specification, via automated type-specific rewriting rules, into a new abstract specification which we call a generator specification. The generator specification is itself parameterised by a number of integer parameters; these are used to characterise a certain region of the parameter space. The solutions of each such generator instance form valid problem instances. We use the parameter tuner irace to explore the space of possible generator parameters, aiming to find parameter values that yield graded instances. We perform an empirical evaluation of our system for five problem classes from CSPlib, demonstrating promising results.Postprin