Placement Algorithms for Hierarchical Cooperative Caching and Other Location Problems

In a large-scale information system, such as a digital library or the world wide web, a set of distributed caches can improve their e ectiveness by cooperating with one another, both in serving each other's requests as well as in deciding what to store. This dissertation explores the potential of such cooperative caching, and provides basic placement algorithms using which the caches can coordinate their storage decisions. The rst part of the dissertation focuses on variants of the placement problem involving a single object. The most well-known of these variants are the facility location problems, which have received considerable attention in the operations research literature due to their widespread applicability. We prove that a simple local search heuristic, proposed about 25 years ago, yields polynomial-time constant-factor approximations for several metric facility location problems. The second part of the dissertation addresses the simultaneous placement of a collection of objects in hierarchical networks. We provide both exact and approximate polynomial-time algorithms for this hierarchical placement problem. Our exact algorithm is based on a reduction to min-cost ow, and does not appear to be practical for large problem sizes. Hence we are motivated to look for simpler approximate algorithms. Our main result is a simple constant-factor approximation algorithm that admits an e cient distributed implementation. The third and nal part of the dissertation describes our simulation experiments which were performed to ascertain the practical potential of cooperative caching, and to investigate the practical performance of various placement and replacement algorithms. Driven by both synthetic and web-trace workloads, these experiments compare several traditional as well as novel caching algorithms. They demonstrate that cooperation improves performance signi cantly, especially when the cache sizes are small. More surprisingly, the experiments show that our amortizing algorithm yields placements that are extremely close, within 5%, to the optimal when the access patterns are stable. We also examine hybrid strategies to cope with changing access patterns. vii Acknowledgments First and foremost, I am deeply indebted to my dissertation supervisor Greg Plaxton. His guidance and encouragement have been invaluable in shaping this dissertation and taking it to completion. Besides supervising this dissertation, Greg has been an amiable mentor and a great friend all along. His infectious enthusiasm together with his `workhard, play-hard' philosophy will continue to inspire me for years to come. I have bene tted greatly from discussions with several other faculty members as well. In particular, David Zuckerman and Martin Wong were very helpful during the initial stages of my graduate studies. David's classes and puzzles were always challenging and reinforced my zeal for research in algorithms. Mike Dahlin and Harrick Vin helped me in my initial forays into experimental work and provided valuable insights. Mike also contributed directly to this dissertation by collaborating with me on the experimental work presented in Chapter 4. I am also grateful to Eva Tardos of Cornell University, as well as Mike Dahlin, Harrick Vin, and David Zuckerman for graciously serving on my dissertation committee and providing encouraging and insightful comments. In addition to Greg and Mike, another researcher who contributed signi cantly to this dissertation is Rajmohan Rajaraman. Raj is a close friend and has been involved with this dissertation right from the beginning; he co-authored the results on the facility location problems in Chapter 2 and the placement problem in Chapter 3. Several colleagues in the computer science department were instrumental in making my graduate life all the more interesting and enjoyable. In particular, the numerous discussions, technical or otherwise, with Ashis Tarafdar, John Havlicek, Kedar Namjoshi, Sriram Rao, Vasilis Samoladas, and Renu Tewari have produced several memorable moments. On the outdoors front, Ramgopal Mettu introduced me to the sport of ix mountain-biking, and Yannis Smaragdakis helped me extensively in my hunt for a used motorcycle. Throughout my stay in Austin, I have been very fortunate to have some great roommates and friends who made my stay a very pleasant and memorable one. I will always remember Navin and his delicious chicken dishes and his ever-surprising takeit-easy policy, Harsha and his infectious cheerfulness (except before the exams!), Vicky and our regular workout sessions, and of course, the a able Randy and his in-depth analysis of the NBA and NFL games. During the early years, the sixth street was an in-thing and Gooty, Santanu, Mouli, and Dan were cool company on several trips. Of late, hanging out with the entire Rio group { Nandu, MP, Gounder, Shail, Satish and Soumya Pillais, Freaky, Gokul, VMS, and several others { has been great fun. Though I missed out on several of their activities due to time constraints, the memories of the card games, the cricket matches, and the birthday parties in J192 will remain for a long while. Aparna has been a wonderful friend ever since she moved into the o ce next door to mine in UA9. If not for her co ee and lively conversations, I wouldnt have spent as much time working in the o ce and this dissertation would have taken that much longer. Of course, I would not have been able to do any of the above without the nancial support provided by the National Science Foundation, The University of Texas at Austin, and the summer internships at Fujitsu Labs of America and Bell Labs. For providing me these internship opportunities and for making them a worthwhile experience, technically or otherwise, I am grateful to Adnan Aziz, Sreeranga P. Rajan, S. Muthukrishnan, and Ganesh Sundaram. Also, I would like to thank Gloria Ramirez and Doug Rockstead, our department sta , for helping me with the various administrative formalities right from day one. Lastly, and most importantly, my parents and my sister Rajitha have been an endless source of love and support throughout my graduate study, and all through my life. In spite of the long years of geographic separation, they { along with my cousin brother Srikanth and the rest of my folks at Hyderabad { never missed a beat in keeping my morale high irrespective of the circumstances. My parents have always given me the x freedom to pursue my interests, and have always backed up my choice with tremendous con dence and a ection; if not for that, I wouldnt be writing this today. This dissertation is dedicated to them. Madhukar Korupolu The University of Texas at Austin August 1999 xi