Impact of information representation on computation

总的来说，我的研究目标是加深我们对信息表示和计算的基本和实际极限的理解。我的研究结合了系统/实验和更多的理论观点。例如，我对生成数据的压缩表示感兴趣。通常，需要从压缩表示中重建原始数据。相反，我的研究重点是保存数据的功能方面。我和我的学生研究如何压缩程序，以便它可以以压缩的形式执行，从而使用更少的内存。我们还将探索压缩数据库，以便它们仍然支持查询操作。这两个应用程序共享查找和利用原始结构化数据中的冗余的基本方法。我们依靠理论和实验评估来确定我们的方法是否实用和有益。 我研究的另一个主要领域是涉及几何对象的计算。当几何输入不精确或不确定时，我对计算感兴趣。例如，离特定地点最近的出租车取决于知道出租车的准确位置。如果这些位置只是大概知道的，那么合适的答案是什么？我还对了解几何对象之间的可见性感兴趣，例如一个地形上的点，以便利用这种可见性关系的结构，例如，放置可以看到一切的警卫。 这些应用需要解决基本的算法问题。在我的研究中，我试图解决这些基本问题，并创建和测试实用的系统。

My research objectives, generally speaking, are to further our understanding of the fundamental and practical limits of information representation and computation. My research combines both systems/experimental and more theoretical viewpoints. For example, I'm interested in producing compressed representations of data. Typically, one requires that the original data can be reconstructed from the compressed representation. My research focuses instead on preserving functional aspects of the data. My students and I investigate how to compress a program so that it can execute in its compressed form, thus using less memory. We also explore compressing databases so that they still support query operations. Both applications share the basic approach of finding and exploiting redundancy in the original structured data. We rely on theoretical and experimental evaluation to determine if our approaches are practical and beneficial. Another main area of my research is in computation involving geometric objects. I'm interested in computation when the geometric input is imprecise or uncertain. For example, the closest taxi to a particular location depends on knowing the precise location of the taxis. If those locations are only known approximately, what is the appropriate answer? I'm also interested in understanding visibility between geometric objects, such as points on a terrain, in order to exploit the structure of this visibility relation, for example, to place guards that can see everything. These applications require the solution of fundamental algorithmic questions. In my research, I try to address these fundamental questions as well as create and test practical systems.