Scheduling Algorithms for Procrastinators

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a \Theta(1) approximation algorithm for the maximum interval stretch.Comment: 12 pages, 3 figure

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs

We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erd\"{o}s-R\'{e}ny graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with respect to the behavior found for classical walks.Comment: 13 pages, 3 figure

Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization

Journal of Heuristics, 19(4), pp.711-728Landscapes’ theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of an especial kind of landscape called elementary landscape. The elementary landscape decomposition of a combinatorial optimization problem is a useful tool for understanding the problem. Such decomposition provides an additional knowledge on the problem that can be exploited to explain the behavior of some existing algorithms when they are applied to the problem or to create new search methods for the problem. In this paper we analyze the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapes’ theory. We prove that the problem can be written as the sum of two elementary components and we give the exact expressions for these components. We use the landscape decomposition to compute autocorrelation measures of the problem, and show some practical applications of the decomposition.Spanish Ministry of Sci- ence and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)

Adaptive access and rate control of CSMA for energy, rate and delay optimization

In this article, we present a cross-layer adaptive algorithm that dynamically maximizes the average utility function. A per stage utility function is defined for each link of a carrier sense multiple access-based wireless network as a weighted concave function of energy consumption, smoothed rate, and smoothed queue size. Hence, by selecting weights we can control the trade-off among them. Using dynamic programming, the utility function is maximized by dynamically adapting channel access, modulation, and coding according to the queue size and quality of the time-varying channel. We show that the optimal transmission policy has a threshold structure versus the channel state where the optimal decision is to transmit when the wireless channel state is better than a threshold. We also provide a queue management scheme where arrival rate is controlled based on the link state. Numerical results show characteristics of the proposed adaptation scheme and highlight the trade-off among energy consumption, smoothed data rate, and link delay.This study was supported in part by the Spanish Government, Ministerio de Ciencia e Innovación (MICINN), under projects COMONSENS (CSD2008-00010, CONSOLIDER-INGENIO 2010 program) and COSIMA (TEC2010-19545-C04-03), in part by Iran Telecommunication Research Center under contract 6947/500, and in part by Iran National Science Foundation under grant number 87041174. This study was completed while M. Khodaian was at CEIT and TECNUN (University of Navarra)

Biosorption of lead (II) and copper (II) metal ions on Cladophora glomerata (L.) Kütz. (Chlorophyta) algae: Effect of algal surface modification

Heavy metals are present in some industrial effluents, being responsible for environmental pollution. Biosorption of heavy metals can be an effective method for the removal of heavy metal ions from wastewaters. In this study Pb(II) and Cu(II) biosorption by Cladophora glomerata algae was investigated in batch system from a binary mixture. The effects of some important parameters such as pH, initial concentration of heavy metals and modification of algae surface by heat/acid treatment on biosorption capacity was studied. The maximum biosorption capacity of Cladophora glomerata was 15.0mg/g at pH 5.0 for Cu(II) and 22.5 mg/g at pH 4.0 for Pb(II) metal ions. The biosorption capacity of Pb(II) and Cu(II) ions on the acid/heat-treated biomass was increased as 1.38 and 1.45 times than untreated form, respectively. The biosorption of Pb (II) and Cu (II) heavy metal ions on Cladophora glomerata appears to be an efficient and low cost alternative to be considered in industrial wastewater treatment