A New Lower Bound for Deterministic Truthful Scheduling
A New Lower Bound for Deterministic Truthful Scheduling
复制标题
确定性真实调度的新下界
DOI：
10.1007/s00453-021-00847-2
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发表时间：
2020
期刊：
影响因子：
1.1
通讯作者：
Diogo Poças
中科院分区：
文献类型：
--
作者：
Yiannis Giannakopoulos;Alexander Hammerl;Diogo Poças
在Makingspan最小化的目标下，我们研究了真正安排M任务的问题，正如Nisan和Ronen的第二次工作所引入的（在：第31届计算理论理论ACM年度ACM年度研讨会（STOC），1999年，1999年所介绍的问题。 ）。在确定性的真实机制的近似值上，缩小[2.618，n]的差距是算法机制设计的臭名昭著的开放问题。 2.414（对于n = 3 \ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasySym} \ usepackage {amsfonts} \ usepackage {amsymb} } \ setLength {\ oddSideMargin} { - 69pt} \ begin {document} $$ n = 3 $$ \ end {document {document {document}）和2.618（对于n→∞\ documentClass [12pt] {12pt] {minimal} {minimal} wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\rightarrow \infty$ Christodoulou等人的$ \ end {document}）。 （2007年），我们更具体地说，即使仅在n = 4 \ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasysym} } \ usepackage {amssymb} \ usepackage {amsbsy} \ usepackage {mathrsfs} \ usepackage {upgreek} \ setLength {\ oddsidemargin} n = 5 \ documentclass [12pt] {minimal} \ usepackage {amsmath} \ usepackage {wasySym} \ usepackage {amsfonts} \ usepackage {amssymb} Ength { \ orddsidemargin} { - 69pt} \ begin {document} $$ n = 5 $$ \ end {document {document}我们已经获得了第一个改进2.755。
We study the problem of truthfully scheduling m tasks to n selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen (in: The 31st Annual ACM symposium on Theory of Computing (STOC), 1999). Closing the current gap of [2.618, n] on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field of algorithmic mechanism design. We provide the first such improvement in more than a decade, since the lower bounds of 2.414 (for n=3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=3$$\end{document}) and 2.618 (for n→∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\rightarrow \infty$$\end{document}) by Christodoulou et al. (in: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2007) and Koutsoupias and Vidali (in: Proceedings of Mathematical Foundations of Computer Science (MFCS), 2007), respectively. More specifically, we show that the currently best lower bound of 2.618 can be achieved even for just n=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=4$$\end{document} machines; for n=5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=5$$\end{document} we already get the first improvement, namely 2.711; and allowing the number of machines to grow arbitrarily large we can get a lower bound of 2.755.