DOCSLIB.ORG

Hierarchical Clustering with Global Objectives: Approximation Algorithms and Hardness Results

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Hierarchical Clustering with Global Objectives: Approximation Algorithms and Hardness Results HIERARCHICAL CLUSTERING WITH GLOBAL OBJECTIVES: APPROXIMATION ALGORITHMS AND HARDNESS RESULTS ADISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Evangelos Chatziafratis June 2020 © 2020 by Evangelos Chatziafratis. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/bb164pj1759 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Tim Roughgarden, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Moses Charikar, Co-Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Li-Yang Tan I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Gregory Valiant Approved for the Stanford University Committee on Graduate Studies. Stacey F. Bent, Vice Provost for Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract Hierarchical Clustering is an important tool for data analysis, used in diverse areas ranging from Phylogenetics in Biology to YouTube video recommendations and everything in between. The term “hierarchical” is used to contrast with “flat” clustering approaches, like k-means or k-center, which only produce one specific partitioning of a data set. Hierarchical Clustering is a way of understanding the overall structure of large data sets by visualizing them as a collection of successively smaller and smaller clusters, capturing di↵erent levels of granularity simultaneously. The end result is a tree, whose internal nodes represent nested clusters and with leaves representing the data points. Despite the plethora of applications and heuristics, the theory behind Hierarchical Clustering was underdeveloped, since no “global” objective function was associated with the final output. A well- formulated objective allows us to compare di↵erent algorithms, measure their quality, explain their success or failure and enables continuous optimization methods with gradient descent. This lack of objectives is in stark contrast with the flat clustering literature, where objectives like k-means, k- median or k-center have been studied intensively starting from the 1950s, leading to a comprehensive theory on clustering. In this thesis, we study approximation algorithms and their limitations, making progress towards building such a theory for objective-based Hierarchical Clustering (HC). For the minimization cost function with pairwise similarities introduced recently by Dasgupta (2016) and its maximization variants, we show how standard tools like Sparsest Cut, Balanced Cut, Max Cut or Max Uncut Bisection can be used in a black box manner, to produce provably good HC and we also complement our algorithms with inapproximability results. Escaping from worst-case analyses, we also study scenarios where extra structure is imposed on the data points (e.g., feature vectors) or qualitative information is provided (e.g., the common triplet or quartet constraints in Phylogenetics). Our results are inspired by geometric ideas (semidefinite programming relaxations, spreading metrics, random projections) and novel connections with ordering Constraint Satisfaction Problems. Overall, this thesis provides state-of-the-art approximation and hardness results for optimizing global HC objectives, reveals unexpected connections with common linkage or graph cut heuristics and advances our understanding of old Phylogenetics problems. As such, we hope it serves the com- munity as the foundation for objective-based Hierarchical Clustering and for future improvements. iv Acknowledgments As I am finishing my thesis from an apartment in New York, I can’t help but thinking how lucky I have been so far, especially throughout those 5 years of my PhD. Featuring a single name on the front cover is merely an understatement, as both this thesis and myself would not be the same without the tremendous help and constant support of several amazing individuals, I had the extreme pleasure to meet along my journey in research and in the academic world. Given that no physical PhD defense ever took place at Stanford, I want to take this opportunity to express my gratitude to the people that helped me during this beautiful journey and, more importantly, made it possible. First and foremost, I can’t thank enough my advisor Tim Roughgarden for all he has done for me over these past 5 years. From my second quarter at Stanford, when I first rotated and worked with Tim, to our productive research trip in London School of Economics during his sabbatical, to our path towards New York in Columbia and my next career steps, Tim has always been extremely supportive and patient of my diverse research pursuits, always ready to provide me with his insightful ideas and advice. I owe him so much for his mentorship and ideas, for inspiring me, for teaching me cool stu↵and helping me improve my communication skills; and all these, done in the casual environment he created for his group (lunches at Ike’s, dinners at NOLA etc.), which allowed me to thrive without ever feeling I was working, rather enjoying research and theory. Outside research, I also want to thank Tim, simply for being lenient with me, accepting my longer-than-usual trips to Greece, without asking questions whether they happened during (early) summer, Christmas, or even March. I also consider myself privileged to have been his unique student simultaneously at Stanford and Columbia, and to have helped with the summer rental car situation in Ikaria and with the cameras and amplifiers during Papafest’s talks and band concert. The second person that I want to thank is Moses Charikar. During the spring quarter of my first year, we started exploring hierarchical clustering, a term I had never heard about back then and, unknowingly, the main chapter in this thesis had already started. Collaborating with Moses and trying to make sense of the variety of clustering questions that appeared on our way over time, has truly been an immense pleasure. His intuition and clarity of thought together with his patience on explaining to me possible ways of attacking the problems have been extremely beneficial. I am also grateful to him for being available for late night Skypes in several occasions and for interrupting his v dinner plans just to answer my texts, admittedly right before the submission deadlines, and finally for battling with the di↵erent timezones when I was in Switzerland or in Sweden and he was in India. I also want to thank Jan Vondrak, not only for our collaboration, but also for being a friendly and approachable person in the Math department, that I always felt comfortable talking to and I could always go with questions and have interesting conversations across many di↵erent topics. Of course, I am glad he also agreed to be the Chair of my thesis committee. I want to thank Greg Valiant for being in my orals committee, for letting me TA several of his courses and for his support during summer 2017. Also, for his direct and casual character that always makes you feel comfortable. I also owe a big thanks to Li-Yang Tan for agreeing to be in my quals and my orals committee and for sharing much of his love and expertise in complexity theory. I also want to thank several professors I had the pleasure to work with for a short period: Virginia Vassilevska Williams for an awesome first rotation, and for her great teaching style, Nisheeth Vishnoi for an inspiring summer internship in EPFL during summer 2016, which taught me a lot and Osman Yagan for several visits to CMU in Silicon Valley and in Pittsburgh and for interesting discussions on network robustness. Outside research, I want to thank Omer Reingold for an amazing class on Playback theater and Kumaran Arul for being an excellent and inspiring piano tutor. Watching Ryan Williams playing guitar, singing and improvising during our Theory Music Tuesday Nights has also been quite the experience! A big role for the development of this thesis was played by my amazing collaborators. First of all, I want to thank Rad Niazadeh for the countless hours we spent drawing trees and clusters on the whiteboard, discussing about how to round SDPs, late-night editing of papers before submissions, and also for giving me career advice. I want to thank Mohammad Mahdian for being an amazing host at Google New York during my summer and winter internships, for the always stimulating conversations that may happen at a microkitchen or while searching for available rooms, over video calls, or even while on vacation in Rhodes, Greece. I want to thank Ioannis Panageas for hosting me in Singapore, for his direct and fun character and for his mathematical depth that helped me explore and appreciate the many interesting connections between deep learning and dynamical systems. Moreover and in no particular order, I also had the pleasure to work with: Neha Gupta, Euiwoong Lee, Sara Ahmadian, Alessandro Epasto, Grigory Yaroslavtsev, Kontantin Makarychev, Sai Ganesh Nagarajan, Xiao Wang, Haris Angelidakis, Avrim Blum, Chen Dan, Pranjal Awasthi, Xue Chen, Aravindan Vijayaraghavan, Osman Yagan, and Joshua Wang.
Load more

Recommended publications
  • FOCS 2005 Program SUNDAY October 23, 2005
    FOCS 2005 Program SUNDAY October 23, 2005 Talks in Grand Ballroom, 17th floor Session 1: 8:50am – 10:10am Chair: Eva´ Tardos 8:50 Agnostically Learning Halfspaces Adam Kalai, Adam Klivans, Yishay Mansour and Rocco Servedio 9:10 Noise stability of functions with low influences: invari- ance and optimality The 46th Annual IEEE Symposium on Elchanan Mossel, Ryan O’Donnell and Krzysztof Foundations of Computer Science Oleszkiewicz October 22-25, 2005 Omni William Penn Hotel, 9:30 Every decision tree has an influential variable Pittsburgh, PA Ryan O’Donnell, Michael Saks, Oded Schramm and Rocco Servedio Sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing 9:50 Lower Bounds for the Noisy Broadcast Problem In cooperation with ACM SIGACT Navin Goyal, Guy Kindler and Michael Saks Break 10:10am – 10:30am FOCS ’05 gratefully acknowledges financial support from Microsoft Research, Yahoo! Research, and the CMU Aladdin center Session 2: 10:30am – 12:10pm Chair: Satish Rao SATURDAY October 22, 2005 10:30 The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics Tutorials held at CMU University Center into `1 [Best paper award] Reception at Omni William Penn Hotel, Monongahela Room, Subhash Khot and Nisheeth Vishnoi 17th floor 10:50 The Closest Substring problem with small distances Tutorial 1: 1:30pm – 3:30pm Daniel Marx (McConomy Auditorium) Chair: Irit Dinur 11:10 Fitting tree metrics: Hierarchical clustering and Phy- logeny Subhash Khot Nir Ailon and Moses Charikar On the Unique Games Conjecture 11:30 Metric Embeddings with Relaxed Guarantees Break 3:30pm – 4:00pm Ittai Abraham, Yair Bartal, T-H.
    [Show full text]
  • Constraint Clustering and Parity Games
    Constrained Clustering Problems and Parity Games Clemens Rösner geboren in Ulm Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Bonn 2019 1. Gutachter: Prof. Dr. Heiko Röglin 2. Gutachterin: Prof. Dr. Anne Driemel Tag der mündlichen Prüfung: 05. September 2019 Erscheinungsjahr: 2019 Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn Abstract Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. We study several clustering objectives. We begin with studying the Euclidean k-center problem. The k-center problem is a classical combinatorial optimization problem which asks to select k centers and assign each input point in a set P to one of the centers, such that the maximum distance of any input point to its assigned center is minimized. The Euclidean k-center problem assumes that the input set P is a subset of a Euclidean space and that each location in the Euclidean space can be chosen as a center. We focus on the special case with k = 1, the smallest enclosing ball problem: given a set of points in m-dimensional Euclidean space, find the smallest sphere enclosing all the points. We combine known results about convex optimization with structural properties of the smallest enclosing ball to create a new algorithm. We show that on instances with rational coefficients our new algorithm computes the exact center of the optimal solutions and has a worst-case run time that is polynomial in the size of the input.
    [Show full text]
  • Implementation of Locality Sensitive Hashing Techniques
    Implementation of Locality Sensitive Hashing Techniques Project Report submitted in partial fulfillment of the requirement for the degree of Bachelor of Technology. in Computer Science & Engineering under the Supervision of Dr. Nitin Chanderwal By Srishti Tomar(111210) to Jaypee University of Information and TechnologyWaknaghat, Solan – 173234, Himachal Pradesh i Certificate This is to certify that project report entitled “Implementaion of Locality Sensitive Hashing Techniques”, submitted by Srishti Tomar in partial fulfillment for the award of degree of Bachelor of Technology in Computer Science & Engineering to Jaypee University of Information Technology, Waknaghat, Solan has been carried out under my supervision. This work has not been submitted partially or fully to any other University or Institute for the award of this or any other degree or diploma. Date: Supervisor’s Name: Dr. Nitin Chanderwal Designation : Associate Professor ii Acknowledgement I am highly indebted to Jaypee University of Information Technology for their guidance and constant supervision as well as for providing necessary information regarding the project & also for their support in completing the project. I would like to express my gratitude towards my parents & Project Guide for their kind co-operation and encouragement which help me in completion of this project. I would like to express my special gratitude and thanks to industry persons for giving me such attention and time. My thanks and appreciations also go to my colleague in developing the project and people who have willingly helped me out with their abilities Date: Name of the student: Srishti Tomar iii Table of Content S. No. Topic Page No. 1. Abstract 1 2.
    [Show full text]
  • Model Checking Large Design Spaces: Theory, Tools, and Experiments
    Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2020 Model checking large design spaces: Theory, tools, and experiments Rohit Dureja Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Recommended Citation Dureja, Rohit, "Model checking large design spaces: Theory, tools, and experiments" (2020). Graduate Theses and Dissertations. 18304. https://lib.dr.iastate.edu/etd/18304 This Thesis is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Model checking large design spaces: Theory, tools, and experiments by Rohit Dureja A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Computer Science Program of Study Committee: Kristin Y. Rozier, Co-major Professor Gianfranco Ciardo, Co-major Professor Samik Basu Robyn Lutz Hridesh Rajan The student author, whose presentation of the scholarship herein was approved by the program of study committee, is solely responsible for the content of this dissertation. The Graduate College will ensure this dissertation is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2020 Copyright © Rohit Dureja, 2020. All rights reserved. ii DEDICATION To my family. iii TABLE OF CONTENTS LIST OF FIGURES . vi LIST OF TABLES . .x ABSTRACT . xi CHAPTER 1. INTRODUCTION . .1 1.1 Motivation .
    [Show full text]
  • Detecting Near-Duplicates for Web Crawling
    WWW 2007 / Track: Data Mining Session: Similarity Search Detecting Near-Duplicates for Web Crawling ∗ Gurmeet Singh Manku Arvind Jain Anish Das Sarma Google Inc. Google Inc. Stanford University [email protected] [email protected] [email protected] ABSTRACT Documents that are exact duplicates of each other (due to Near-duplicate web documents are abundant. Two such mirroring and plagiarism) are easy to identify by standard documents differ from each other in a very small portion checksumming techniques. A more difficult problem is the that displays advertisements, for example. Such differences identification of near-duplicate documents. Two such docu- are irrelevant for web search. So the quality of a web crawler ments are identical in terms of content but differ in a small increases if it can assess whether a newly crawled web page portion of the document such as advertisements, counters is a near-duplicate of a previously crawled web page or not. and timestamps. These differences are irrelevant for web In the course of developing a near-duplicate detection sys- search. So if a newly-crawled page Pduplicate is deemed a tem for a multi-billion page repository, we make two research near-duplicate of an already-crawled page P , the crawl en- contributions. First, we demonstrate that Charikar's finger- gine should ignore Pduplicate and all its out-going links (in- printing technique is appropriate for this goal. Second, we tuition suggests that these are probably near-duplicates of P 1 present an algorithmic technique for identifying existing f- pages reachable from ). Elimination of near-duplicates bit fingerprints that differ from a given fingerprint in at most saves network bandwidth, reduces storage costs and im- k bit-positions, for small k.
    [Show full text]
  • Time-Release Cryptography from Minimal Circuit Assumptions
    Time-release Cryptography from Minimal Circuit Assumptions Samuel Jaques∗ Hart Montgomeryy Arnab Royz Abstract Time-release cryptography requires problems that take a long time to solve and take just as long even with significant computational resources. While time-release cryptography originated with the seminal paper of Rivest, Shamir and Wagner (’96), it has gained special visibility recently due to new time-release primitives, like verifiable delay functions (VDFs) and sequential proofs of work, and their novel blockchain applications. In spite of this recent progress, security definitions remain inconsistent and fragile, and foundational treatment of these primitives is scarce. Relationships between the various time-release primitives are elusive, with few connections to standard cryptographic assumptions. We systematically address these drawbacks. We define formal notions of sequential functions, the building blocks of time-release cryptography. The new definitions are robust against change of machine models, making them more amenable to complexity theoretic treatment. We demonstrate the equivalence of various types of sequential functions under standard cryptographic assumptions. The time-release primitives in the literature (such as those defined by Bitansky et al. (ITCS ’16)) imply that these primitives exist, as well as the converse. However, showing that a given construction is a sequential function is a hard circuit lower bound problem. To our knowledge, no results show that standard cryptographic assumptions imply any sequen- tiality. For example, repeated squaring over RSA groups is assumed to be sequential, but nothing connects this conjecture to standard hardness assumptions. To circumvent this, we construct a function that we prove is sequential if there exists any sequential function, without needing any specific knowledge of this hypothetical function.
    [Show full text]
  • Moses Charikar Stanford University
    Moses Charikar Stanford University Friday, March 22, 2019 3:00 pm Luddy Hall, Rm. 1106 Importance Sampling in High Dimensions via Hashing Abstract: Locality sensitive hashing (LSH) is a popular technique for nearest neighbor search in high dimensional data sets. Recently, a new view at LSH as a biased sampling technique has been fruitful for density estimation problems in high dimensions. Given a set of points and a query point, the goal (roughly) is to estimate the density of the data set around the query. One way to formalize this is by kernel density estimation: Given a function that decays with distance and represents the "influence" of a data point at the query, sum up this influence function over the data set. Yet another way to formalize this problem is by counting the number of data points within a certain radius of the query. While these problems can easily be solved by making a linear pass over the data, this can be prohibitive for large data sets and multiple queries. Can we preprocess the data so as to answer queries efficiently? This talk will survey several recent papers that use locality sensitive hashing to design unbiased estimators for such density estimation problems and their extensions. This talk will survey joint works with Arturs Backurs, Piotr Indyk, Vishnu Natchu, Paris Syminelakis and Xian (Carrie) Wu. Biography: Moses Charikar is the Donald E. Knuth professor of Computer Science at Stanford University. He obtained his PhD from Stanford in 2000, spent a year in the research group at Google, and was on the faculty at Princeton from 2001-2015.
    [Show full text]
  • Approximation Algorithms for Grammar-Based
    Approximation Algorithms for Grammar-Based Data Compression by Eric Lehman Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2002 © Eric Lehman, MMII. All rights reserved. The author hereby grants to MIT permission to reproduce and E'AKER distribute publicly paper and electronic copies of this thesis dm STSITTUCE in whole or in part. ArPR 1 6 2002 LIBRARIES Author ............... Department of Electrical Engineering and Computer Science February 1, 2002 Certified by ....................... Madhu Sudan Associate Professor of Electrical Enginjering and Computer Science Thesjs Supevisor Accepted by ............. ...... Arthur C. Smith Chairman, Department Committee on Graduate Students 2 Approximation Algorithms for Grammar-Based Data Compression by Eric Lehman Submitted to the Department of Electrical Engineering and Computer Science on February 1, 2002, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract This thesis considers the smallest grammar problem: find the smallest context-free grammar that generates exactly one given string. We show that this problem is intractable, and so our objective is to find approximation algorithms. This simple question is connected to many areas of research. Most importantly, there is a link to data compression; instead of storing a long string, one can store a small grammar that generates it. A small grammar for a string also naturally brings out under- lying patterns, a fact that is useful, for example, in DNA analysis. Moreover, the size of the smallest context-free grammar generating a string can be regarded as a computable relaxation of Kolmogorov complexity.
    [Show full text]
  • Rajeev Motwani
    THEORY OF COMPUTING, Volume 8 (2012), pp. 55–68 www.theoryofcomputing.org SPECIAL ISSUE IN HONOR OF RAJEEV MOTWANI Rajeev Motwani (1962-2009) Prabhakar Raghavan∗ Received: September 13, 2010; published: March 31, 2012. Abstract: Rajeev Motwani was a pre-eminent theoretical computer scientist of his genera- tion, a technology thought leader, an insightful venture capitalist, and a mentor to some of the most influential entrepreneurs in Silicon Valley in the first decade of the 21st century. This article presents an overview of Rajeev’s research, and provides a window to his early life and the various influences that shaped his research and professional career—it is a small celebration of his wonderful life and many achievements. ACM Classification: K.2/People, F.2.2 AMS Classification: 01A70, 68-00 Key words and phrases: biography 1 Early Life and Education Rajeev Motwani was born on March 24, 1962 in the Indian city of Jammu to Lieutenant Colonel Hotchand Motwani, an officer in the Indian Army, and Namita Motwani (nee´ Sushila). His family included brothers Sanjeev and Suneev. Given his father’s army career, Rajeev’s family moved often and lived in various parts of India before settling down in New Delhi. Those who knew Rajeev as a young boy remember him as an avid reader. When Rajeev was seven, his father was stationed in the scenic town of Devlali near Mumbai, India. His family would walk a kilometer to the local library to get books, and the seven-year-old Rajeev would be seen reading the books ∗Based on contributions by Sanjeev Arora, Gautam Bhargava, Piotr Indyk, Asha Jadeja, Sanjeev Motwani, Prabhakar Raghavan, and G.
    [Show full text]
  • Practical Hash Functions for Similarity Estimation and Dimensionality Reduction
    Practical Hash Functions for Similarity Estimation and Dimensionality Reduction Søren Dahlgaard Mathias Bæk Tejs Knudsen University of Copenhagen / SupWiz University of Copenhagen / SupWiz [email protected] [email protected] Mikkel Thorup University of Copenhagen [email protected] Abstract Hashing is a basic tool for dimensionality reduction employed in several aspects of machine learning. However, the perfomance analysis is often carried out under the abstract assumption that a truly random unit cost hash function is used, without concern for which concrete hash function is employed. The concrete hash function may work fine on sufficiently random input. The question is if they can be trusted in the real world where they may be faced with more structured input. In this paper we focus on two prominent applications of hashing, namely similarity estimation with the one permutation hashing (OPH) scheme of Li et al. [NIPS’12] and feature hashing (FH) of Weinberger et al. [ICML’09], both of which have found numerous applications, i.e. in approximate near-neighbour search with LSH and large-scale classification with SVM. We consider the recent mixed tabulation hash function of Dahlgaard et al. [FOCS’15] which was proved theoretically to perform like a truly random hash function in many applications, including the above OPH. Here we first show im- proved concentration bounds for FH with truly random hashing and then argue that mixed tabulation performs similar when the input vectors are not too dense. Our main contribution, however, is an experimental comparison of different hashing schemes when used inside FH, OPH, and LSH.
    [Show full text]
  • STOC ’98 to Qualify for the Early Registration Fee, Your Registra- Tion Application Must Be Postmarked by Thursday, April 30, 1998
    Registration for STOC '98 To qualify for the early registration fee, your registra- tion application must be postmarked by Thursday, April 30, 1998. The non-student registration fee in- cludes the Saturday night reception, the Sunday night STOC '98 business meeting, the Monday night banquet, coffee breaks, lunches, and a copy of the proceedings. The student fee includes all of the above except the banquet. Mail the form below, along with credit card informa- tion or a check or money order in U.S. currency drawn through a U.S. bank, made payable to ACM/STOC'98. STOC '98 Computer Science Program University of Texas at Dallas P.O. Box 830688, EC 31 Richardson, TX 75083{0688 Name Address Email Phone FAX Special Needs (Please specify) Affiliation (as you wish it to appear on your name tag): The 30th Annual Please circle one amount below and fill in your member- ACM Symposium on ship number if appropriate: # . Theory of Computing Registrants in the \Other" category will automatically become SIGACT members for a period of one year. Fee (US$) after April 30 ACM or SIGACT Member 315 390 Student 125 190 Dallas, Texas Other 390 465 May 24 { May 26, 1998 Check your dietary preference: Kosher 2 Vegetarian 2 No Restriction 2 Number of additional proceedings $54 each: Number of additional Banquet tickets $55 each: Total included: $ Sponsored by ACM SIGACT Credit Card Information (if applicable): VISA / MasterCard / American Express (circle) with support from Microsoft one Card # Exp. Date: Signature Hotel Reservations Deadline: April 30, 1998 The conference will be held at the Fairmont Hotel, Dal- las, Texas.
    [Show full text]
  • A Constant Factor Approximation Algorithm for Fault-Tolerant K- Median
    25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2014) Portland, Oregon, USA 5-7 January 2014 Volume 1 of 2 Editor: C. Chekuri ISBN: 978-1-5108- 1330-4 Printed from e-media with permission by: Curran Associates, Inc. 57 Morehouse Lane Red Hook, NY 12571 Some format issues inherent in the e-media version may also appear in this print version. Copyright© (2014) by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics. All rights reserved. Printed by Curran Associates, Inc. (2015) For permission requests, please contact SIAM: Society for Industrial and Applied Mathematics at the address below. SIAM 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Phone: (215) 382-9800 Fax: (215) 386-7999 [email protected] Additional copies of this publication are available from: Curran Associates, Inc. 57 Morehouse Lane Red Hook, NY 12571 USA Phone: 845-758-0400 Fax: 845-758-2634 Email: [email protected] Web: www.proceedings.com TABLE OF CONTENTS VOLUME 1 A CONSTANT FACTOR APPROXIMATION ALGORITHM FOR FAULT-TOLERANT K- MEDIAN ................................................................................................................................................................................1 Mohammadtaghi Hajiaghayi, Wei Hu, Jian Li, Shi Li, Barna Saha IMPROVED APPROXIMATION ALGORITHM FOR TWO-DIMENSIONAL BIN PACKING ............................. 13 Nikhil Bansal, Arindam Khan A MAZING 2+ ε APPROXIMATION FOR UNSPLITTABLE FLOW ON A PATH .................................................
    [Show full text]