a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...

Submodular-function maximization is a central problem in combinatorial optimization, generalizing many important NP-hard problems including Max Cut in digraphs, graphs and hypergraphs, certain constraint satisfaction problems, maximum-entropy sampling, and maximum facility-location problems. Our main result is that for any k ≥ 2 and any ε > 0, there is a natural local-search algorithm which has...

The maximin share guarantee is, in the context of allocating indivisible goods to a set of agents, a recent fairness criterion. A solution achieving a constant approximation of this guarantee always exists and can be computed in polynomial time. We extend the problem to the case where the goods collectively received by the agents satisfy a matroidal constraint. Polynomial approximation algorith...

This paper incorporates Corrected Transient Energy Margin (CTEM) to the clearing of coupled energy and reactive power market in the form of multi objective framework which includes two objective functions. The first one is the minimization of offer cost of generators for their active power generation in energy market plus Total Payment Function (TPF) of generators for reactive power compensatio...

Traditional rejection/reduction tests used in branch-and-prune methods for nonlinear systems usually are based on various forms of the interval Newton operator and constraint propagation techniques. Hence, they are relatively costly. This paper considers an additional phase of a branchand-prune method for the exclusion of regions not containing any solutions. Low-discrepancy sequences of Sobol ...

This paper presents a multi-periodic, multi-echelon blood supply chain network consisting of blood donors, mobile collection units, local blood centers, main blood centers and demand points in which the local and main blood centers are subject to random failure in dispatching blood products to demand points. The problem has two objectives including minimization of the total chain costs and maxi...

During the epidemic outbreak period, number of infected people increased explosively. In order to effectively contain further spread and treat people, it is necessary make reasonable planning for treatment distribution materials. this paper, a multi-objective mixed-integer programming model integrated design emergency medical material networks developed, in which location points, allocation mat...

MapReduce (MR) algorithms for maximizing monotone, submodular functions subject to a cardinality constraint (SMCC) are currently restricted the use of linear-adaptive (non-parallelizable) algorithm GREEDY. Low-adaptive do not satisfy requirements these distributed MR frameworks, thereby limiting their performance. We study SMCC problem in setting and propose first with sublinear adaptive comple...

Hazardous chemicals are harmful to the people around them during their storage, especially when an accident occurs. The allocation and scheduling of emergency materials, therefore, is important imperative rescue services. Due characteristics dangerous goods, storage risk hazardous in networks always exists, which threatens surrounding residents. To reduce terms networks, collaborative optimizat...