Dynamic Boolean Formula Evaluation

We present a linear space data structure for Dynamic Evaluation of k-CNF Boolean Formulas which achieves O(m^{1-1/k}) query and variable update time where m is the number of clauses in the formula and clauses are of size at most a constant k. Our algorithm is additionally able to count the total number of satisfied clauses. We then show how this data structure can be parallelized in the PRAM model to achieve O(log m) span (i.e. parallel time) and still O(m^{1-1/k}) work. This parallel algorithm works in the stronger Binary Fork model. We then give a series of lower bounds on the problem including an average-case result showing the lower bounds hold even when the updates to the variables are chosen at random. Specifically, a reduction from k-Clique shows that dynamically counting the number of satisfied clauses takes time at least n^{(2?-3)/6 ?{2k} -1 -o(?k)}, where 2 ? ? < 2.38 is the matrix multiplication constant. We show the Combinatorial k-Clique Hypothesis implies a lower bound of m^{(1-k^{-1/2})(1-o(1))} which suggests our algorithm is close to optimal without involving Matrix Multiplication or new techniques. We next give an average-case reduction to k-clique showing the prior lower bounds hold even when the updates are chosen at random. We use our conditional lower bound to show any Binary Fork algorithm solving these problems requires at least ?(log m) span, which is tight against our algorithm in this model. Finally, we give an unconditional linear space lower bound for Dynamic k-CNF Boolean Formula Evaluation

PGGA: A predictable and grouped genetic algorithm for job scheduling

This paper presents a predictable and grouped genetic algorithm (PGGA) for job scheduling. The novelty of the PGGA is twofold: (1) a job workload estimation algorithm is designed to estimate a job workload based on its historical execution records, (2) the divisible load theory (DLT) is employed to predict an optimal fitness value by which the PGGA speeds up the convergence process in searching a large scheduling space. Comparison with traditional scheduling methods such as first-come-first-serve (FCFS) and random scheduling, heuristics such as a typical genetic algorithm, Min-Min and Max-Min indicates that the PGGA is more effective and efficient in finding optimal scheduling solutions

How proofs are prepared at Camelot

We study a design framework for robust, independently verifiable, and workload-balanced distributed algorithms working on a common input. An algorithm based on the framework is essentially a distributed encoding procedure for a Reed--Solomon code, which enables (a) robustness against byzantine failures with intrinsic error-correction and identification of failed nodes, and (b) independent randomized verification to check the entire computation for correctness, which takes essentially no more resources than each node individually contributes to the computation. The framework builds on recent Merlin--Arthur proofs of batch evaluation of Williams~[{\em Electron.\ Colloq.\ Comput.\ Complexity}, Report TR16-002, January 2016] with the observation that {\em Merlin's magic is not needed} for batch evaluation---mere Knights can prepare the proof, in parallel, and with intrinsic error-correction. The contribution of this paper is to show that in many cases the verifiable batch evaluation framework admits algorithms that match in total resource consumption the best known sequential algorithm for solving the problem. As our main result, we show that the $k$-cliques in an $n$-vertex graph can be counted {\em and} verified in per-node $O(n^{(\omega+\epsilon)k/6})$ time and space on $O(n^{(\omega+\epsilon)k/6})$ compute nodes, for any constant $\epsilon>0$ and positive integer $k$ divisible by $6$, where $2\leq\omega<2.3728639$ is the exponent of matrix multiplication. This matches in total running time the best known sequential algorithm, due to Ne{\v{s}}et{\v{r}}il and Poljak [{\em Comment.~Math.~Univ.~Carolin.}~26 (1985) 415--419], and considerably improves its space usage and parallelizability. Further results include novel algorithms for counting triangles in sparse graphs, computing the chromatic polynomial of a graph, and computing the Tutte polynomial of a graph.Comment: 42 p

Multi-objective scheduling of Scientific Workflows in multisite clouds

Clouds appear as appropriate infrastructures for executing Scientific Workflows (SWfs). A cloud is typically made of several sites (or data centers), each with its own resources and data. Thus, it becomes important to be able to execute some SWfs at more than one cloud site because of the geographical distribution of data or available resources among different cloud sites. Therefore, a major problem is how to execute a SWf in a multisite cloud, while reducing execution time and monetary costs. In this paper, we propose a general solution based on multi-objective scheduling in order to execute SWfs in a multisite cloud. The solution consists of a multi-objective cost model including execution time and monetary costs, a Single Site Virtual Machine (VM) Provisioning approach (SSVP) and ActGreedy, a multisite scheduling approach. We present an experimental evaluation, based on the execution of the SciEvol SWf in Microsoft Azure cloud. The results reveal that our scheduling approach significantly outperforms two adapted baseline algorithms (which we propose by adapting two existing algorithms) and the scheduling time is reasonable compared with genetic and brute-force algorithms. The results also show that our cost model is accurate and that SSVP can generate better VM provisioning plans compared with an existing approach.Work partially funded by EU H2020 Programme and MCTI/RNP-Brazil (HPC4E grant agreement number 689772), CNPq, FAPERJ, and INRIA (MUSIC project), Microsoft (ZcloudFlow project) and performed in the context of the Computational Biology Institute (www.ibc-montpellier.fr). We would like to thank Kary Ocaña for her help in modeling and executing the SciEvol SWf.Peer ReviewedPostprint (author's final draft