Minimizing Average Flow-Time under Knapsack Constraint
نویسندگان
چکیده
We give the first logarithmic approximation for minimizing average flow-time of jobs in the subset parallel machine setting (also called the restricted assignment setting) under a single knapsack constraint. In a knapsack constraint setting, each job has a profit, and the set of jobs which get scheduled must have a total profit of at least a quantity Π. Our result extends the work of Gupta, Krishnaswamy, Kumar and Segev (APPROX 2009) who considered the special case where the profit of each job is unity. Our algorithm is based on rounding a natural LP relaxation for this problem. In fact, we show that one can use techniques based on iterative rounding.
منابع مشابه
Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product
We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizin...
متن کاملSubmodular Optimization with Submodular Cover and Submodular Knapsack Constraints
We investigate two new optimization problems — minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint (submodular knapsack). We are motivated by a number of real-world applications in machine learning including sensor placement and data subset selection, which require ...
متن کاملMaximizing expected utility over a knapsack constraint
The expected utility knapsack problem is to pick a set of items whose values are described by random variables so as to maximize the expected utility of the total value of the items picked while satisfying a constraint on the total weight of items picked. We consider the following solution approach for this problem: (i) use the sample average approximation framework to approximate the stochasti...
متن کاملMaximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard. In this paper, we give the firs...
متن کاملPropagating Knapsack Constraints in Sublinear Time
We develop an efficient incremental version of an existing cost-based filtering algorithm for the knapsack constraint. On a universe of n elements, m invocations of the algorithm require a total ofO(n log n+mk log(n/k)) time, where k ≤ n depends on the specific knapsack instance. We show that the expected value of k is significantly smaller than n on several interesting input distributions, hen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014