Non-Preemptive Scheduling on Machines with Setup Times

Consider the problem in which n jobs that are classified into k types are to be scheduled on m identical machines without preemption. A machine requires a proper setup taking s time units before processing jobs of a given type. The objective is to minimize the makespan of the resulting schedule. We design and analyze an approximation algorithm that runs in time polynomial in n, m and k and computes a solution with an approximation factor that can be made arbitrarily close to 3/2.Comment: A conference version of this paper has been accepted for publication in the proceedings of the 14th Algorithms and Data Structures Symposium (WADS

Structural insights into Clostridium perfringens delta toxin pore formation

Clostridium perfringens Delta toxin is one of the three hemolysin-like proteins produced by C. perfringens type C and possibly type B strains. One of the others, NetB, has been shown to be the major cause of Avian Nectrotic Enteritis, which following the reduction in use of antibiotics as growth promoters, has become an emerging disease of industrial poultry. Delta toxin itself is cytotoxic to the wide range of human and animal macrophages and platelets that present GM2 ganglioside on their membranes. It has sequence similarity with Staphylococcus aureus β-pore forming toxins and is expected to heptamerize and form pores in the lipid bilayer of host cell membranes. Nevertheless, its exact mode of action remains undetermined. Here we report the 2.4 Å crystal structure of monomeric Delta toxin. The superposition of this structure with the structure of the phospholipid-bound F component of S. aureus leucocidin (LukF) revealed that the glycerol molecules bound to Delta toxin and the phospholipids in LukF are accommodated in the same hydrophobic clefts, corresponding to where the toxin is expected to latch onto the membrane, though the binding sites show significant differences. From structure-based sequence alignment with the known structure of staphylococcal α-hemolysin, a model of the Delta toxin pore form has been built. Using electron microscopy, we have validated our model and characterized the Delta toxin pore on liposomes. These results highlight both similarities and differences in the mechanism of Delta toxin (and by extension NetB) cytotoxicity from that of the staphylococcal pore-forming toxins

Identifying The Optimal Face Of A Network Linear Program With A Globally Convergent Interior Point Method

. Based on recent convergence results for the affine scaling algorithm for linear programming, we investigate strategies to identify the optimal face of a minimum cost network flow problem. In the computational experiments described, one of the proposed optimality indicators is used to implement an early stopping criterion in dlnet, an implementation of the dual affine scaling algorithm for solving minimum cost network flow problems. We conclude from the experiments that the new indicator is far more robust than the one used in earlier versions of dlnet. Key words. Linear programming, minimum cost network flow, indicator, affine scaling algorithm, computer implementation. AMS(MOS) subject classifications. 65-05, 65F10, 65K05, 65Y05, 90C05, 90C06, 90C35 1. Introduction. The dual affine scaling (das) algorithm [3] has been shown to perform well in practice on linear programming problems [1, 2, 7, 8], large-scale network flow problems [13], and large-scale assignment problems [11, 12]. ..

Fifty years of scheduling: a survey of milestones

Scheduling has become a major field within operational research with several hundred publications appearing each year. This paper explores the historical development of the subject since the mid 1950s when the landmark publications started to appear. A discussion of the main topics of scheduling research for the past five decades is provided, highlighting the key contributions that helped shape the subject. The main topics covered in the respective decades are combinatorial analysis, branch and bound, computational complexity and classification, approximate solution algorithms, and enhanced scheduling models

A New Graph Parameter to Measure Linearity

International audienceSince its introduction to recognize chordal graphs by Rose, Tarjan, and Lueker, Lexicographic Breadth First Search (LexBFS) has been used to come up with simple, often linear time, algorithms on various classes of graphs. These algorithms are usually multi-sweep algorithms; that is they compute LexBFS orderings σ1,…,σkσ1,…,σk , where σiσi is used to break ties for σi+1σi+1 . Since the number of LexBFS orderings for a graph is finite, this infinite sequence {σi}{σi} must have a loop, i.e. a multi-sweep algorithm will loop back to compute σjσj , for some j. We study this new graph invariant, LexCycle(G), defined as the maximum length of a cycle of vertex orderings obtained via a sequence of LexBFS ++ . In this work, we focus on graph classes with small LexCycle. We give evidence that a small LexCycle often leads to linear structure that has been exploited algorithmically on a number of graph classes. In particular, we show that for proper interval, interval, co-bipartite, domino-free cocomparability graphs, as well as trees, there exists two orderings σσ and ττ such that σ=LexBFS+(τ)σ=LexBFS+(τ) and τ=LexBFS+(σ)τ=LexBFS+(σ) . One of the consequences of these results is the simplest algorithm to compute a transitive orientation for these graph classes. It was conjectured by Stacho [2015] that LexCycle is at most the asteroidal number of the graph class, we disprove this conjecture by giving a construction for which LexCycle(G)>an(G)LexCycle(G)>an(G) , the asteroidal number of G