We consider the problem of minimizing the makespan(Cmax) on m identical parallel batch processing machines. The batch processing machine can process up to B jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the job...

Given n independent integer-valued random variables X1, X2, ..., Xn and an integer C, we study the fundamental problem of computing the probability that the sum X = X1+X2+...+Xn is at most C. We assume that each random variable Xi is implicitly given by an oracle Oi, which given two input integers n1, n2 returns the probability of n1 ≤ Xi ≤ n2. We give the first deterministic fully polynomial-t...

We consider the problem of computing shortest paths in three-dimensions in the presence of a single-obstacle polyhedral terrain, and present a new algorithm that for any p ≥ 1, computes a (c + ε)approximation to the Lp-shortest path above a polyhedral terrain in O( ε log n log log n) time and O(n log n) space, where n is the number of vertices of the terrain, and c = 2(p−1)/p. This leads to a F...

In this paper, we address the scheduling problem with rejection in which we can choose a subset of jobs to process. Choosing not to process any job incurs a corresponding penalty. We consider the following problem for the first time: scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties on identical parallel machines, where the number of...

For anti-ferromagnetic 2-spin systems, a beautiful connection has been established, namely that the following three notions align perfectly: the uniqueness of Gibbs measures in infinite regular trees, the decay of correlations (also known as spatial mixing), and the approximability of the partition function. The uniqueness condition implies spatial mixing, and an FPTAS for the partition functio...

We study the Travelling Salesperson (TSP) and Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths a certain length. It has been shown that transportation networks, on which TSP STP naturally occur for various applications logistics, typically have small While it was previously these problem...

We introduce a novel model for “flows over time” which captures the behavior of cars traveling through a road network better than previous models. We show that computing an optimal solution in the new model is NP-hard and present an LP-based algorithm which we evaluate with several experiments on real world data of road networks and generated requests. Among other things we compare the quality ...

In this paper we introduce a graph problem, called Maximum Node Clustering (MNC). We prove that the problem is strongly NP -complete and show that it can be approximated in polynomial time within a ratio arbitrarily close to 2. For the special case where the graph is a tree, we prove that the problem is weakly NP -complete as it generalizes the 0/1 Knapsack problem and is solvable in pseudopoly...

We study the following algorithmic problem: given n points within a finite d-dimensional box, what is the smallest number of extra points that need to be added, to ensure that every d-dimensional unit box is either empty, or contains at least k points. We motivate the problem through a possible application to data privacy. We show that minimizing the number of extra points to be added is strong...

We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding. As an application of these techniques, we present a linear-storage Polynomial Time Approximation Scheme (PTAS) and a Fully Polynomial Time Approximation Sche...