Corrigendum: Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling

2021 ◽  
Author(s):  
Varun Gupta ◽  
Benjamin Moseley ◽  
Marc Uetz ◽  
Qiaomin Xie
Keyword(s):  
Greedy Algorithm ◽  
Online Algorithms ◽  
Upper Bound ◽  
Objective Function Value ◽  
Stochastic Scheduling ◽  
Performance Guarantee ◽  
Performance Bound ◽  
Unrelated Machines ◽  
Release Times ◽  
A Performance

This corrigendum fixes an incorrect claim in the paper Gupta et al. [Gupta V, Moseley B, Uetz M, Xie Q (2020) Greed works—online algorithms for unrelated machine stochastic scheduling. Math. Oper. Res. 45(2):497–516.], which led us to claim a performance guarantee of 6 for a greedy algorithm for deterministic online scheduling with release times on unrelated machines. The result is based on an upper bound on the increase of the objective function value when adding an additional job [Formula: see text] to a machine [Formula: see text] (Gupta et al., lemma 6). It was pointed out by Sven Jäger from Technische Universität Berlin that this upper bound may fail to hold. We here present a modified greedy algorithm and analysis, which leads to a performance guarantee of 7.216 instead. Correspondingly, also the claimed performance guarantee of [Formula: see text] in theorem 4 of Gupta et al. for the stochastic online problem has to be corrected. We obtain a performance bound [Formula: see text].

scholarly journals Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint

2021 ◽  
Vol 5 (1) ◽  
pp. 1-22
Author(s):  
Jing Tang ◽  
Xueyan Tang ◽  
Andrew Lim ◽  
Kai Han ◽  
Chongshou Li ◽  
...  
Keyword(s):  
Approximation Algorithms ◽  
Greedy Algorithm ◽  
Branch And Bound ◽  
Upper Bound ◽  
Optimization Problem ◽  
Approximation Factor ◽  
Real World Application ◽  
Efficiency Of Algorithms ◽  
Knapsack Constraint ◽  
Submodular Maximization

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we show that this algorithm can achieve an approximation factor of 0.405, which significantly improves the known factors of 0.357 given by Wolsey and (1-1/e)/2\approx 0.316 given by Khuller et al. More importantly, our analysis closes a gap in Khuller et al.'s proof for the extensively mentioned approximation factor of (1-1/\sqrte )\approx 0.393 in the literature to clarify a long-standing misconception on this issue. Second, we enhance the modified greedy algorithm to derive a data-dependent upper bound on the optimum. We empirically demonstrate the tightness of our upper bound with a real-world application. The bound enables us to obtain a data-dependent ratio typically much higher than 0.405 between the solution value of the modified greedy algorithm and the optimum. It can also be used to significantly improve the efficiency of algorithms such as branch and bound.

On Performance Bounds for Control Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 311-314 ◽  
Author(s):  
J. Rissanen ◽  
R. Durbeck
Keyword(s):  
Sensitivity Analysis ◽  
Nonlinear Control ◽  
Control Systems ◽  
Nonlinear Control Systems ◽  
Performance Bounds ◽  
Performance Bound ◽  
Lyapunov’S Second Method ◽  
Lurie Problem ◽  
A Performance

A technique based on Lyapunov’s second method is described for deriving bounds for the performance of nonlinear control systems. As an illustration, a performance bound is derived for systems associated with the so-called Lurie problem. As opposed to conventional sensitivity analysis, performance bounds are also determined for systems designed using grossly inaccurate models.

ESTIMATED AND ACCURATE SYSTEM RELIABILITIES OF A MAINTAINABLE COMPUTER NETWORK SUBJECT TO MAINTENANCE BUDGET

2012 ◽  
Vol 29 (03) ◽  
pp. 1240021 ◽  
Author(s):  
YI-KUEI LIN ◽  
PING-CHEN CHANG
Keyword(s):  
Lower Bound ◽  
Branch And Bound ◽  
Upper Bound ◽  
System Reliability ◽  
Performance Index ◽  
Computer Network ◽  
Estimation Procedure ◽  
Reliability Performance ◽  
A Performance

This paper proposes a performance index to evaluate the capability of a maintainable computer network (MCN) that is required to send d units of data from the source to the sink through two paths within time T. The proposed system reliability performance index quantifies the probability that a MCN delivers a sufficient capacity with a maintenance budget no greater than B. Two procedures are integrated in the algorithm — an estimation procedure for estimated system reliability and an adjusting procedure utilizing the branch-and-bound approach for accurate system reliability. Subsequently, the estimated system reliability with lower bound and upper bound, and accurate system reliability can be derived by applying the recursive sum of disjoint products (RSDP) algorithm.

A performance guarantee for the greedy set-partitioning algorithm

1984 ◽  
Vol 21 (4) ◽  
pp. 409-415 ◽  
Author(s):  
E. G. Coffman ◽  
M. A. Langston
Keyword(s):  
Set Partitioning ◽  
Performance Guarantee ◽  
Partitioning Algorithm ◽  
A Performance

On Random Greedy Triangle Packing

10.37236/1296 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
David A. Grable
Keyword(s):  
Greedy Algorithm ◽  
General Problem ◽  
Upper Bound ◽  
Triple System ◽  
Final Number ◽  
Edge Disjoint ◽  
Partial Triple System ◽  
Maximal Packing

The behaviour of the random greedy algorithm for constructing a maximal packing of edge-disjoint triangles on $n$ points (a maximal partial triple system) is analysed with particular emphasis on the final number of unused edges. It is shown that this number is at most $n^{7/4+o(1)}$, "halfway" from the previous best-known upper bound $o(n^2)$ to the conjectured value $n^{3/2+o(1)}$. The more general problem of random greedy packing in hypergraphs is also considered.

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