Online Computation and Competitive Analysis

Transcription

1 Online Computation and Competitive Analysis Allan Borodin University of Toronto Ran El-Yaniv Technion - Israel Institute of Technology I CAMBRIDGE UNIVERSITY PRESS

2 Contents Preface page xiii 1 Introduction to Competitive Analysis: The List Accessing Problem Basic Ideas and Terminology The List Accessing Problem The Sleator-Tarjan Result The Potential Function Method Some Lower Bounds The List Factoring Technique Historical Notes and Open Questions 19 2 Introduction to Randomized Algorithms: The List Accessing Problem The Competitive Ratio of Randomized Algorithms Algorithm BIT Algorithm RMTF: Barely Random Versus Random List Factoring-Phase Partitioning Revisited COMB: An -Competitive Algorithm Historical Notes and Open Questions 29 3 Paging: Deterministic Algorithms Some Paging Algorithms The (h, k)-paging Problem List Accessing Algorithms as Paging Algorithms LFD - An Optimal Offline Paging Algorithm Marking and Conservative Algorithms and the Competitiveness of LRU, CLOCK, FIFO, and FWF LIFO and LFU Are Not Competitive The Full Access Cost Model 40 vii

3 viii CONTENTS 3.8 Theory Versus Practice Historical Notes and Open Questions 42 4 Paging: Randomized Algorithms Randomized Competitive Analysis The Competitiveness of RANDOM The MARK Algorithm A Lower Bound for Randomized Paging Algorithms Historical Notes and Open Questions 52 5 Alternative Paging Models: Beyond Pure Competitive Analysis The Access Graph Model Dynamic Access Graphs and Experimental Studies Distributional Paging Models Historical Notes and Open Questions 75 6 Game Theoretic Foundations Games in Extensive and Strategic Forms Randomized Strategies: Mixed, Behavioral, and General Equivalence Theorems for Linear Games and Games of Perfect Recall An Application to Paging and Competitive Analysis Historical Notes and Open Questions 95 7 Request-Answer Games Request-Answer Games Randomized Adversaries Relating the Adversaries Historical Notes and Open Questions Competitive Analysis and Zero-Sum Games Two-Person Zero-Sum Games On Generalizations of the Minimax Theorem for Infinite Games Yao's Principle: A Technique for Obtaining Lower Bounds Paging Revisited Historical Notes Metrical Task Systems Formulation of (Metrical) Task Systems An 8(iV - 1)-Competitive Traversal Algorithm A2N-1 Lower Bound 128

4 CONTENTS IX 9.4 An Optimal Work Function MTS Algorithm A Randomized Algorithm for a Uniform MTS A Randomized Polylogarithmic Competitive Algorithm for Any MTS Historical Notes and Open Questions The ^-Server Problem The Formulation of the Model Some Basic Aspects of the ^-Server Problem A Deterministic Lower Bound ^-Servers on a Line and a Tree An Efficient 3-Competitive 2-Server Algorithm for Euclidean Spaces Balancing Algorithms The ^-Server Work Function Algorithm On Generalizations of the ^-Server Conjecture That Fail Historical Notes and Open Questions Randomized A>Server Algorithms Oblivious Adversaries and Two Randomized ^-Server Algorithms for the Circle A Lower Bound Against an Adaptive-Online Adversary The-Cat and Rat Game and Applications to Randomized ^-Server Algorithms The Harmonic Random Walk The HARMONIC it-server Algorithm on an Arbitrary Metric Space The Resistive Approach Historical Notes and Open Questions Load Balancing Defining the Problem Online Algorithms for Load Balancing of Permanent Jobs Formulating the Machine Assignment Problem as a Generalized Virtual Circuit Routing Problem Load Balancing of Temporary Jobs Bin Packing Historical Notes and Open Questions Call Admission and Circuit Routing Specifying the Problem 226

5 X CONTENTS 13.2 Throughput Maximization for Permanent Calls in Networks with Large Edge Capacities Throughput Maximization for Limited Duration Calls Experimental Results Call Admission for Particular Networks: The Disjoint Paths Problem The Disjoint Paths Problem: A Lower Bound for a Difficult Network Routing on Optical Networks Path Coloring for Particular Networks A Lower Bound for Path Coloring on the Brick Wall Graph Historical Notes and Open Problems Search, Trading, and Portfolio Selection Online Search and One-Way Trading Online Portfolio Selection Two-Way Trading: Statistical Adversaries and "Money Making" Algorithms Two-Way Trading and the Fixed Fluctuation Model Weighted Portfolio Selection Algorithms Historical Notes and Open Questions On Decision Theories and the Competitive Ratio Certainty, Risk, and Strict Uncertainty Decision Making Under Strict Uncertainty The Competitive Ratio Axioms Characterization of the Competitive Ratio Characterizations of the Classical Criteria for Strict Uncertainty An Example - The Leasing Problem Decision Making Under Risk Bayesian Approaches for Decision Making Under Uncertainty Historical Notes and Open Questions 348 A Glossary 355 B Stochastic Analyses for List Accessing Algorithms 357 C The Harmonic Random Walk and Its Connection to Electrical Networks 361

6 CONTENTS XI D Proof of Lemmas 5.4 and 5.5 in Theorem 5.11: FAR Is a Uniformly Optimal Online Paging Algorithm 364 D.I Proof of Lemma 5.4: Type 1 Reps and the Construction of T' 364 D.2 Proof of Lemma 5.5: Type 2 Reps and the Construction of H 365 E Some Tools from Renewal Theory 369 E. 1 Renewal Processes 369 E.2 Wald's Equation 370 E.3 The Elementary Renewal Theorem 373 F Proof of Theorem 13.14: Disjoint Paths in an Array 375 F.I Short Distance Calls 375 F.2 Long Distance Calls 376 G Some Tools from the Theory of Types 379 H Two Technical Lemmas 382 Bibliography 389 Index 403