Approximation algorithms for hard optimization problems in multi-omics research and operations research

多组学研究和运筹学中硬优化问题的近似算法

• 批准号: RGPIN-2019-05258
• 负责人: Lin, Guohui
• 金额: $ 2.99万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738149
• 关键词: Approximation; algorithms; hard; optimization; problems

The proposed research program focuses on designing efficient algorithms with provable performance for computational optimization problems inspired by real world applications, in particular from multi-omics research and operations research. When facing a challenging real world application, the typical process is first to formulate the problem mathematically, to pursue the optimization of a specified objective function. The optimization problem is then studied to understand its level of difficulty and to design algorithms supported by a rigorous analysis of its efficiency, performance and correctness. But most of our target problems arising from challenging applications cannot be solved optimally in polynomial time, unless P = NP. We follow the line of main stream research to study the in-/approximability of the problems and to design approximation algorithms for the problems. Additionally, we will study the fixed parameter tractability of the problems and seek to pioneer the fixed parameter approximability. Approximation algorithms run in polynomial time and produce solutions that are guaranteed to be within a certain factor of the optimal solution. The study of the design and analysis of approximation algorithms has multi-faceted impact: 1) due to the intractability of the target optimization problem, an approximation algorithm at least gives a way to find a near-optimal solution with provable guarantee; 2) although the worst-case performance guarantee may appear disappointing, an approximation algorithm can frequently perform really well on real world instances; and 3) most importantly, the developed algorithmic tools and design-and-analysis techniques can be generally useful, even if the approximation algorithm by itself may not be very practical. While approximation algorithms are positive results for approaching an NP-hard problem, it is also important to study the limit of such approximation, known as the hardness of approximation or inapproximability. By proving lower bounds on approximability of the problems, we achieve deeper insights on the spectrum of the NP-hard optimization problems. Such insights can in turn be used to develop new and better approximation algorithms. The tractability and the approximability of the problem could change along with the (often multiple) parameters and/or output. Fixed parameter tractability has been extensively investigated, but results on how the approximability of the problems changes along with the parameters in the input or output are limited. The study on approximation algorithms with both running time and performance ratio depending on a parameter k has the same multi-faceted aspects as stated in the above, and additionally provides insights on the parameter k and subsequently another deeper understanding of the internal spectrum of the target optimization problem.

提出的研究计划侧重于设计具有可证明性能的高效算法，以解决受现实世界应用，特别是多组学研究和运筹学启发的计算优化问题。当面对一个具有挑战性的现实世界应用时，典型的过程是首先用数学方法将问题表述出来，追求特定目标函数的优化。然后对优化问题进行研究，了解其困难程度，并通过严格分析其效率，性能和正确性来设计算法。但是，我们的大多数目标问题都不能在多项式时间内得到最优解决，除非P = NP。我们遵循主流研究的思路，研究问题的内/近似性，并设计问题的近似算法。此外，我们将研究问题的固定参数可跟踪性，并寻求开拓固定参数逼近性。近似算法在多项式时间内运行，产生的解保证在最优解的某个因子范围内。研究近似算法的设计与分析具有多方面的影响：1)由于目标优化问题的难解性，近似算法至少给出了一种寻找具有可证明保证的近最优解的方法；2)尽管最坏情况下的性能保证可能看起来令人失望，但近似算法通常可以在现实世界的实例中表现得很好；3)最重要的是，开发的算法工具和设计分析技术通常是有用的，即使近似算法本身可能不是很实用。虽然近似算法是接近np困难问题的积极结果，但研究这种近似的极限也很重要，即近似的硬度或不可近似性。通过证明问题近似性的下界，我们对NP-hard优化问题的范围有了更深入的了解。这样的见解可以反过来用于开发新的和更好的近似算法。问题的可跟踪性和近似性可能随着（通常是多个）参数和/或输出而改变。固定参数可跟踪性已经得到了广泛的研究，但是关于问题的逼近性如何随着输入或输出参数的变化而变化的结果是有限的。对运行时间和性能比都取决于参数k的近似算法的研究与上述相同，具有多面性，并且还提供了对参数k的见解，从而对目标优化问题的内部谱有了更深入的理解。