On-Line Competitive Algorithms

摘要：Marek Chrobak Proposal Number：9988360机构：加州大学河滨分校实践中出现的优化问题通常是固有的(在线)；即，输入数据在计算之前不可用，而是作为请求序列给出，每个请求必须在接收到下一个请求之前得到服务。一个经典的例子是两级存储系统中的(捕获)问题。现代计算机体系结构通过将最频繁访问的数据项存储在高速缓存中来增强存储器性能，高速缓存是具有非常短的访问时间的小缓冲存储器。当请求的项r不在高速缓存中时--这一事件称为(故障)--高速缓存算法将r存储在高速缓存中。如果缓存已满，则算法需要决定从缓存中逐出哪个项，以便为r腾出空间。该决定是(在线)做出的，而不知道未来的请求。当然，目标是将故障数量降至最低。由于信息不完全，在线算法一般不能计算出最优解。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)，它被定义为所有请求序列的最大值，以及由在线算法计算的解与最优(离线)解之间的比率。因此，竞争比为1.5的算法总是计算出最小值的50%以内的解。本研究涉及在线算法的竞争分析，分为三个项目。第一个项目是研究几个已知的特定在线问题，包括k-服务器问题、文件缓存等。这项工作的目标是为这些问题开发有效的竞争算法，并建立它们的竞争比的匹配下界。在第二个项目中讨论了竞争分析中更基本的问题。这里主要关注的是在线算法的设计和分析技术。在这个方向上最有前途的新兴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，以确定它们对其他问题的适用性。第三个项目是探索最近为缓存问题引入的竞争分析的一些扩展：访问图、分散对手和松散竞争。除了解决这一领域的一些尚待解决的问题外，该项目还将专注于使这些新模型适应缓存以外的在线问题(例如文件迁移)，并在适当的情况下设计和研究其他特定于问题的模型。

AbstractPI: Marek ChrobakProposal Number: 9988360Institution: University of California-RiversideOptimization problems that arise in practice are often inherently (online); that is, the input data is not available prior to computation but, instead, is given as a sequence of requests each of which must be served before the next one is received. A classical example is the (catching) problem in two-level memory systems. Modern computer architectures enhance memory performance by storing the most frequently accessed data items in a cache, which is a small buffer memory with very short access time. When a requested item r is not in the cache -- an event referred to as a (fault) -- the caching algorithm stores r in the cache. If the cache is full, the algorithm needs to decide which item to evict from the cache to make room for r. This decision is made (online), without the knowledge of future requests. Naturally, the goal is to minimize the number of faults. Due to incomplete information, online algorithms cannot, in general, compute optimal solutions. This brings up the issue of performance evaluation: how do we tell good algorithms from bad ones? One measure of the quality of online algorithms is their (competitive ratio), defined as the maximum, over all request sequences, and of the ratios between the solution computed by the online algorithm and the optimal (offline) solution. Thus, an algorithm with competitive ratio, says, 1.5, always computes a solution that is within 50% of the minimum. This research deals with the competitive analysis of online algorithms and is divided into three projects. The first project is to study several known, specific online problems, including the k-server problem, file caching, and others. The objectives of this work are to develop efficient competitive algorithms for these problems and to establish matching lower bounds on their competitive ratios. More fundamental issues in competitive analysis are addressed in the second project. The main focus here is on the techniques for the design and analysis of online algorithms. The most promising, emerging ideas in this direction include the work-function algorithm (and its extensions) and the primal-dual method. Both of these techniques, as well as some other, have been successfully applied to specific online problems, but the mechanism behind their success is still poorly understood, and they still require an in-depth study to determine their applicability to other problems. The third project is to explore some extensions of the competitive analysis that have been recently introduced for the caching problem: access graphs, diffuse adversaries, and loose competitiveness. In addition to work on some remaining open problems in this area, this project will also focus on adapting these new models to online problems other than caching (for example, file migration), and, if appropriate, on designing and studying other problem-specific models.