The Online Disjoint Set Cover Problem and its Applications

Given a universe $U$ of $n$ elements and a collection of subsets $\mathcal{S}$ of $U$, the maximum disjoint set cover problem (DSCP) is to partition $\mathcal{S}$ into as many set covers as possible, where a set cover is defined as a collection of subsets whose union is $U$. We consider the online DSCP, in which the subsets arrive one by one (possibly in an order chosen by an adversary), and must be irrevocably assigned to some partition on arrival with the objective of minimizing the competitive ratio. The competitive ratio of an online DSCP algorithm $A$ is defined as the maximum ratio of the number of disjoint set covers obtained by the optimal offline algorithm to the number of disjoint set covers obtained by $A$ across all inputs. We propose an online algorithm for solving the DSCP with competitive ratio $\ln n$. We then show a lower bound of $\Omega(\sqrt{\ln n})$ on the competitive ratio for any online DSCP algorithm. The online disjoint set cover problem has wide ranging applications in practice, including the online crowd-sourcing problem, the online coverage lifetime maximization problem in wireless sensor networks, and in online resource allocation problems.Comment: To appear in IEEE INFOCOM 201

Optimal file allocation problems for distributed data bases in unreliable computer networks

"December, 1982"Bibliography: leaf [6]"ONR/N00014-77-C-0532 (NR 041-519)Moses Ma

Decision-based genetic algorithms for solving multi-period project scheduling with dynamically experienced workforce

The importance of the flexibility of resources increased rapidly with the turbulent changes in the industrial context, to meet the customers’ requirements. Among all resources, the most important and considered as the hardest to manage are human resources, in reasons of availability and/or conventions. In this article, we present an approach to solve project scheduling with multi-period human resources allocation taking into account two flexibility levers. The first is the annual hours and working time regulation, and the second is the actors’ multi-skills. The productivity of each operator was considered as dynamic, developing or degrading depending on the prior allocation decisions. The solving approach mainly uses decision-based genetic algorithms, in which, chromosomes don’t represent directly the problem solution; they simply present three decisions: tasks’ priorities for execution, actors’ priorities for carrying out these tasks, and finally the priority of working time strategy that can be considered during the specified working period. Also the principle of critical skill was taken into account. Based on these decisions and during a serial scheduling generating scheme, one can in a sequential manner introduce the project scheduling and the corresponding workforce allocations

An Introduction to Mechanized Reasoning

Mechanized reasoning uses computers to verify proofs and to help discover new theorems. Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals. We introduce mechanized reasoning to economists in three ways. First, we introduce mechanized reasoning in general, describing both the techniques and their successful applications. Second, we explain how mechanized reasoning has been applied to economic problems, concentrating on the two domains that have attracted the most attention: social choice theory and auction theory. Finally, we present a detailed example of mechanized reasoning in practice by means of a proof of Vickrey's familiar theorem on second-price auctions

Program Verification of Numerical Computation

These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that outline the definitions and rules upon which VPC is based. The initial motivation of this project was to address some practical issues of computation, especially of numerically intensive programs that are commonplace in computer models. The project evolved into a wider area for program construction as proofs leading to a model of inference in a more general sense. Some basic results of machine arithmetic are derived as a demonstration of VPC

Validating Sample Average Approximation Solutions with Negatively Dependent Batches

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling method) and averaging the obtained objective values. State-of-the-art methods for lower-bound estimation generate batches of scenarios for the SAA problems independently. In this paper, we describe sampling methods that produce negatively dependent batches, thus reducing the variance of the sample-averaged lower bound estimator and increasing its usefulness in defining a confidence interval for the optimal objective value. We provide conditions under which the new sampling methods can reduce the variance of the lower bound estimator, and present computational results to verify that our scheme can reduce the variance significantly, by comparison with the traditional Latin hypercube approach

A GPU Simulation for Evolution-Communication P Systems with Energy Having no Antiport Rules

Evolution-Communication P system with energy (ECPe systems) is a cell- like variant P system which establishes a dependence between evolution and communi- cation through special objects, called `energy,' produced during evolution and utilized during communication. This paper presents our initial progress and e orts on the im- plementation and simulation of ECPe systems using Graphics Processing Units (GPUs). Our implementation uses matrix representation and operations presented in a previous work. Speci cally, an implementation of computations on ECPe systems without antiport rules is discussed.Junta de Andalucía P08-TIC-04200Ministerio de Ciencia e Innovación TIN2012-3743

A threshold based dynamic data allocation algorithm - a Markov Chain model approach

In this study, a new dynamic data allocation algorithm for non-replicated Distributed Database Systems (DDS), namely the threshold algorithm, is formulated and proposed. The threshold algorithm reallocates data with respect to changing data access patterns. The proposed algorithm is distributed in the sense that each node autonomously decides whether to transfer the ownership of a fragment in DDS to another node or not. The transfer decision depends on the past accesses of the fragment. Each fragment continuously migrates ftom the node where it is not accessed locally more than a certain number of past accesses, namely a threshold value. The threshold algorithm is modeled for a fragment of the database as a finite Markov chain with constant node access probabilities. In the model, a special case, where all nodes have equal access probabilities except one with a different access probability, is analyzed. It has been shown that for positive threshold values the fragment will tend to remain at the node with the higher access probability. It is also shown that the greater the threshold values are, the greater the tendency of the fragment to remain at the node with higher access probability will be. The threshold algorithm is especially suitable for a DDS where data access pattern changes dynamically