Online Competitive Algorithms

实际中出现的优化问题通常是固有的在线问题；也就是说，输入数据在计算之前不可用，而是以请求序列的形式给出，每个请求必须在接收下一个请求之前被服务。典型的例子是两级存储系统中的缓存问题。现代计算机体系结构通过将频繁访问的数据项存储在高速缓冲存储器中来增强存储器性能，高速缓冲存储器是一种小缓冲存储器。存储在高速缓存中的存储位置可以被快速访问。对不在缓存中的内存位置的请求被称为错误或未命中，并且需要更多的时间。在每次内存访问后，在线缓存算法需要决定是否将请求的项放入缓存中，如果是，则从缓存中逐出哪个项。目标是最小化缓存故障的数量，由于信息不完全，在线算法通常无法计算出最优解。这就带来了性能评估的问题：我们如何区分好的算法和坏的算法？衡量在线算法质量的一个指标是它们的竞争比，即对所有请求序列而言，在线算法计算的解与最优(离线)解之间的比率的最大值。因此，一个竞争比为1.5的算法总是计算出一个在最小值50%以内的解。本文研究在线算法的竞争性分析。第一个方向是研究设计和分析在线算法的一般技术。在这里，最有希望的想法包括功函数算法(及其扩展)和原始对偶方法。这两种技术以及其他一些技术已经成功地应用于特定的在线问题，但它们成功背后的机制仍然鲜为人知，它们仍然需要深入研究才能确定它们对其他问题的适用性。另一个方向是研究竞争分析的几个扩展，包括访问图(用于缓存)、扩散对手、松散竞争力和资源增加。这项工作集中在与这些模型相关的一些开放问题，使这些模型适应其他在线问题，并设计新的特定于问题的模型。这位研究人员还在继续研究竞争分析中的几个经典问题，包括k-服务器问题、缓存和调度问题的几个版本、k-Medium问题等。这些努力的主要目标是为这些问题开发有效的竞争算法，并建立竞争比的匹配下界。

Optimization problems that arise in practice are often inherentlyonline; that is, the input data is not available prior tocomputation but, instead, is given as a sequence of requestseach of which must be served before the next one is received.A classical example is the caching problem in two-level memorysystems. Modern computer architectures enhance memory performanceby storing frequently accessed data items in a cache, which isa small buffer memory. Memory locations stored in the cachecan be accessed quickly. Requests to memory locations that arenot in the cache are called faults or misses, and take muchmore time. After each memory access, an online caching algorithmneeds to decide whether to put the requested item in the cache,and if so, which item to evict from the cache. The objectiveis to minimize the number of cache faults.Due to incomplete information, online algorithms cannot, in general,compute optimal solutions. This brings up the issue of performanceevaluation: how do we tell good algorithms from bad ones? One measureof the quality of online algorithms is their competitive ratio,defined as the maximum, over all request sequences, of the ratiosbetween the solution computed by the online algorithm and the optimal(offline) solution. Thus, an algorithm with competitive ratio, say,1.5, always computes a solution that is within 50% of the minimum.This research deals with the competitive analysis of online algorithms.Several research directions are being explored. The first directionis to study general techniques for the design and analysis of onlinealgorithms. Here, the most promising ideas include thework-function algorithm (and its extensions) and the primal-dual method.Both of these techniques, as well as some other, have been successfullyapplied to specific online problems, but the mechanism behind theirsuccess is still poorly understood, and they still require an in-depthstudy to determine their applicability to other problems. Anotherdirection is to study several extensions of the competitive analysis,including access graphs (for caching), diffuse adversaries, loosecompetitiveness and resource augmentation. This work focuses on some openproblems related to these models, on adapting these models to otheronline problems, and on designing new problem-specific models. Theinvestigator is also continuing his work on several classicalproblems in competitive analysis, including the k-serverproblem, several versions of caching and scheduling problems,the k-median problem, and other. The main goals of these effortsare to develop efficient competitive algorithms for these problemsand to establish matching lower bounds on the competitive ratios.