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FAST approximation algorithmS FOR KNAPSACK AND SUM OF SUBSET PROBLEMS

JOURNAL OF THE ACM 1975年第4期22卷 463-468页

作者： IBARRA, OH KIM, CE UNIV MINNESOTA DEPT COMP INFORMATION & CONTROL SCI114 MAIN ENGN BLDGMINNEAPOLISMN 55455

Given a positive integer M and n pairs of positive integers [formula omitted], maximize the [formula omitted] subject to the constramts [formula omitted] and δi = 0 or 1 This is the well-known 0/1 knapsack problem An... 详细信息

Given a positive integer M and n pairs of positive integers [formula omitted], maximize the [formula omitted] subject to the constramts [formula omitted] and δ_i = 0 or 1 This is the well-known 0/1 knapsack problem An algorithm is presented which finds for any 0 < ϵ < 1 an approximate solution P satisfying [formula omitted] is the desired optimal sum Moreover, for any fixed ϵ, the algorithm has time complexity O(n log n) and space complexity O(n) Modification of the algorithm for the unbounded knapsack problem where the δ_i's can be any nonnegative integer results in a O(n) computing time A hnear-time algorithm is also obtained for a special class of 0/1 knapsack problems having the property that p_i/c_i is the same for all 1 ≤ i ≤ n. © 1975, ACM. All rights reserved.

关键词： approximation algorithm knapsack problem P-complete problem polynomial time algorithm sum of subset problem

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On two—processor scheduling of one— or two—unit time tasks with precedence constraints

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Journal of Cybernetics 1975年第3期5卷 87-100页

作者： Ibarra, Oscar H. Kim, Chul E. Department of Computer Science University of Minnesota Minneapolis MN 55455 United States

This paper is concerned with the problem of scheduling on two processors tasks with 1- or 2-unit execution time and having arbitrary precedence constraints. An analysis is made of the algorithm (called f LPTS-schedule) which chooses as the next task to be scheduled, that task for which the sum of the execution times of all its successors is maximal. It is shown that LPTS produces a schedule with an error where f * and f̂are the finish times of an optimal and LPTS schedules, respectively. An example is given which shows that the error bound is tight, even for the case when all tasks have 1-unit execution time. A comparison of the LPTS algorithm with other scheduling algorithms is also presented. © 1975 Taylor & Francis Group, LLC.

关键词： approximation algorithm Coffman-Graham algorithm Finish time Longest-path-schedule LPTS-schedule Multiprocessing problem P-complete problem Two processor case with 1- or 2-unit time tasks

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