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

Implementation of a Database System with Boolean Algebra Constraints

This thesis describes an implementation of a constraint database system with constraints over a Boolean Algebra of sets. The system allows within the input database as well as the queries equality, subset-equality and monotone inequality constraints between Boolean Algebra terms built up using the operators of union, intersection and complement. Hence the new system extends the earlier DISCO system, which only allowed equality and subset-equality constraints between Boolean algebra variables and constants. The new system allows Datalog with Boolean Algebra constraints as the query lan- guage. The implementation includes an extension of Naive and Semi-Naive evaluation methods for Datalog programs and algebraic optimization techniques for relational algebra formulas. The thesis also includes three example applications of the new system in the area of family tree genealogy, genome map assembly, and two-player game analysis. In each of these three cases the optimization provides a significant improvement in the running time of the queries. Advisor: Peter Z. Reves

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

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.Comment: 13 pages, 6 figure

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