814 References R. E. Tarjan. Data structures and network algorithms. CBMS-NSF Regional Conference Series in Applied Mathematics 44. SocieW for Industrial and Applied Mathematics, 1983. R. E. Tarjan. <strong>Algorithm</strong>ic design. Communications of the ACM, 30:3 (1987), 204- 212. A. Tucker. Coloring a family of circular arcs. SIAM J. Applied Matheraatics, 29:3 (November 1975), 493-502. V. Vazirani. Approximation <strong>Algorithm</strong>s. Springer-Verlag, 2001. O. Veksler. Efficient Graph-Based Energy Minimization Methods in Computer Vision. Ph.D. thesis, Corne!l University, 1999. M. Waterman. Introduction to Computational Biology: Sequences, Maps and Genomes. Chapman Hall, 1995. D. J. Watts. Six Degrees: The Science of a Connected Age. Norton, 2002. K. Wayne. A new property and faster algorithm for baseball elimination. SIAM J. Discrete Mathematics, !4:2 (2001), 223-229. J. W. J. Williams. <strong>Algorithm</strong> 232 (Heapsort). Communications of the ACM, 7 (1964), 347-348. Index A page number ending in ex refers to a topic that is discussed in an exercise. Numbers 3-Coloring Problem NP-completeness, 487-490 as optimization problem, 782 ex 3-Dimensional Matching Problem NP-completeness, 481-485 polynomial time approximation algorithm for, 656ex problem, 481 3-SAT Problem, 459-460 assignments in, 459, 594-596 ex as Constraint Satisfaction Problem, 500 in Lecture Planning exercise, 503-504 ex MAX-3 -SAT algorithm design and analysis for, 725-726 good assignments in, 726-727 notes, 793 problem, 724-725 random assignment for, 725-726, 787 ex NP completeness, 471 polynomial space algorithm for, 532 Quantified. See QSAT (Quantified 3 -SAT) reductions in, 459-463 4-Dimensional Matching Problem, 507 ~ A Aarts, E., 705 (a,b)-skeletons, 5!7-518 ex ABL (average bits per letter) in encoding, 165 Absolute weight of edges, 671 Ad hoc networks, 435-436 ex Adaptive compression schemes, 177 Add lists in planning problems, 534, 538 Adenine, 273 Adjacency lists, 87-89, 93 Adjacency matrices, 87-89 Adopters in human behaviors, 523 ex Ads advertising policies, 422-423 ex Strategic Advertising Problem, 508-509 ex Affiliation network graphs, 76 Agglomerative clustering, 159 Ahuja, Ravindra K., 449-450 Airline route maps, 74 Airline Scheduling Problem, 387 algorithm for analyzing, 390-391 designing, 389-390 problem, 387-389 Alignment, sequence. See Sequence alignment Allocation random, in load balancing, 761-762 register, 486 resource. See Resource allocation Alon, N., 793-794 Alternating paths in Bipartite Matching Problem, 370 Althofer, Ingo, 207 Ambiguity in Morse code, 163 Ancestors lowest common, 96 in trees, 77 Anderberg, M., 206 Annealing, 669-670 Anshelevich, E., 706 Antigens, blood, 418-419 ex Apartments, expense sharing in, 429-430 ex Appalachian Trail exercise, 183- 185 ex Appel, K., 490 Approximate medians, 791 ex Approximate time-stamps, 196- 197 ex Approximation algorithms, 599-600 in caching, 751 greedy algorithms for Center Selection Problem, 606-612 Interval Scheduling Problem, 649-651 ex load balancing, 600-606 Set Cover Problem, 612-617 Knapsack Problem, 644 algorithm analysis for, 646-647 algorithm design for, 645-646 problem, 644-645 linear programming and rounding. See Linear programming and rounding load balancing, 637 algorithm design and analysis for, 638-643 problem, 637-638
816 Index Approximation algorithms (cont.) Maximum-Cut Problem, 676, 683-684 algorithm analysis for, 677-679 algorithm design for, 676-677 for graph partitioning, 680-681 notes, 659 pricing methods Disjoint Paths Problem, 624- 630 Vertex Cover Problem, 618-623 Approximation thresholds, 660 Arbitrage opportunities for shortest paths, 291 Arbitrarily good approximations for Knapsack Problem, 644 algorithms for analyzing, 646-647 designing, 645-646 problem, 644-64-5 Arborescences, minimum-cost, 116, 177 greedy algorithms for analyzing, 181-183 designing, 179-181 problem, 177-179 Arc coloring. See Circular-Arc Coloring Problem Arithmetic coding, 176 Arora, S., 660 Arrays in dynamic programming, 258-259 for heaps, 60-61 in Knapsack Problem, 270-271 in Stable Matching <strong>Algorithm</strong>, 42-45 for Union-Find structure, 152-153 ASCII code, 162 Assignment penalty in Image Segmentation Problem, 683 Assignments 3-SAT, 459,594-596 ex in bipartite matching, 15 for linear equations mod 2, 780-781 ex in load balancing, 637 for MAX-3-SAT problem, 725-726, 787 ex partial, 591-594 ex wavelength, 486 Astronomical events, 325-326ex Asymmetric distances in Traveling Salesman Problem, 479 Asymmetry of NP, 495-497 Asymptotic order of growth, 55-36 in common functions, 40-42 lower bounds, 37 notes, 70 properties of, 38-40 tight bounds, 37-38 upper bounds, 36-37 Asynchronous algorithms Bellman-Ford, 299 Gale-Shapley, 10 Atmospheric science experiment, 426-427 dx Attachment costs, 143 Auctions combinatorial, 511 ex one-pass, 788-789 ex Augment algorithm, 542-343,346 Augmentation along cycles, 643 Augmenting paths, 342-343 choosing, 352 algorithm analysis in, 354-356 algorithm design in, 552-354 algorithm extensions in, 556-357 finding, 412 ex in Minimum-Cost Perfect Matching Problem, 405 in neighbor relations, 680 Average bits per letter (ABL) in encoding, 165 Average-case analysis, 31,707 Average distances in networks, 109-110 ~ Awerbuch, B., 659 Azar, Y., 659 B Back-up sets for networks, 435-436 ex Backoff protocols, 793 Backward edges in residual graphs, 341-342 Backward-Space-Efficient-Alignment, 286-287 Backwards analysis, 794 Bacon, Kevin, 448 ex Bank cards, fraud detection, 246-247 ex Bar-Yehuda, R., 659 Barabasi, A. L., !13 Barter economies, 521-522 ex Base of logarithms, 41 Base-pairing in DNA, 273-275 Base stations for cellular phones, 190ex, 430-431 ex for mobile computing, 417-418 ex Basebal! Elimination Problem, 400 algorithm design and analysis for, 402-403 characterization in, 403-404 notes, 449 problem, 400-401 Bases, DNA, 273-275 Beckmann, M., 706 Belady, Les, 133,206 Bell, T. C., 206 Bellman, Richard, 140, 292, 335 Bellman-Ford algorithm in Minimum-Cost Perfect Matching Problem, 408 for negative cycles in graphs, 301-303 for router paths, 298-299 for shortest paths, 292-295 Berge, C., 113 Berlekamp, E. R., 551 Bern, M., 659 Bertsekas, D. backoff protocols, 793 shortest-path algorithm, 336 Bertsimas, Dimitris, 336 Best achievable bottleneck rate, 198-199 ex Best-response dynamics, 690, 693-695 definitions and examples, 691-693 Nash equilibria and, 696-700 notes, 706 problem, 690-691 questions, 695-696 Best valid partners in Gale-Shapley algorithm, 10-11 BFS (breadth-first search), 79-82 for bipartiteness, 94-96 for directed graphs, 97-98 implementing, 90-92 in planning problems, 541 for shortest paths, 140 BGP (Border Gateway Protocol), 301 Bicriteria shortest path problems, 530 Bidding agents, 789 ex Bids in combinatorial auctions, 511 ex in one-pass auctions, 788-789 ex Big-improvement-flips, 678 Billboard placement, 307-309 ex Bin-packing, 651 ex Binary search in arrays, 44 in Center Selection Problem, 610 sublinear time in, 56 Binary trees nodes in, 10Sex for prefix codes, 166-169 Biology genome mapping, 279, 521 ex, 787 ex RNA Secondary Structure Prediction Problem, 272-273 algorithm for, 275-278 notes, 335 problem, 273-275 sequences in, 279 Bipartite graphs, 14-16, 337, 368-370 2-colorability of, 487 notes, 449 testing for, 94-96 Bipartite Matching Problem, 337, 367 algorithm for analyzing, 369-371 designing, 368 extensions, 371-373 costs in, 404-405 algorithm design and analysis for, 405-410 algorithm extensions for, 410-411 problem, 405 description, 14-16 in Hopfield neural networks, 703 ex neighbor relations in, 679-680 in packet switching, 798 problem, 368 Bipartiteness testing, breadth-first search for, 94-96 Bits in encoding, 162-163 Blair Witch Project, 183-185 ex Blocking in Disjoint Paths Problem, 627 in Interval Scheduling Problem, 650ex in packet switching, 798-799 Blood types, 418-419 ex Boese, K., 207 Boles, David, 503 ex Bollobas, B., 113 Boolean formulas with quantification, 534 in Satisfiability Problem, 459-460 Border Gateway Protocol (BGP), 301 Borodin, Allan caching, 794 greedy algorithms, 207 Bottleneck edges, 192 ex Bottlenecks in augmenting paths, 342-345,352 in communications, 198-199 ex Bounds in asymptotic order of growth lower, 37 tight, 37-38 upper, 36-37 Chernoff, 758-760 for load balancing, 762 for packet routing, 767-769 in circulations, 382-384, 414ex in Load Balancing Problem algorithm analysis for, 601-604 algorithm design for, 601 algorithm extensions for, 604-606 problem, 600 Boxes, nesting arrangement for, 434-435 ex Boykov, Yuri, 450, 706 Breadth-first search (BFS), 79-82 for bipartiteness, 94-96 for directed graphs, 97-98 implementing, 90-92 in planning problems, 541 for shortest paths, 140 Broadcast Time Problem, 527-528 ex Brute-force search and dynamic pmgrammning, 252 in worst-case running times, 31-32 Buffers in packet switching, 796-801 Butterfly specimens, 107-108 ex Cache hits and misses, 132-133, 750 Cache Maintenance Problem greedy algorithms for designing and analyzing, 133-136 extensions, 136-137 Index 817 notes, 206 problem, 131-133 Caching optimal greedy algorithm design and analysis for, 133-136 greedy algorithm extensions for, 136-137 problem, 131-133 randomized, 750-751 marking algorithm for, 753- 755 notes, 794 problem, 750-752 randomized algorithm for, 755-758 Capacity and capacity conditions in circulation, 380, 383 of cuts, 346, 348 of edges, 338 in integer-valued flows, 351 in network models, 338-339 of nodes, 420-421 ex for preflows, 357 in residual graphs, 342 Card guessing with memory, 721-722 without memory, 721 Carpool scheduling, 431 ex Carter, L. J., 794 Cascade processes, 523 ex Cellular phone base stations, 190 ex, 430-431 ex Center Selection Problem, 606 algorithms for, 607-612 limits on approximability, 644 local search for, 700-702 ex notes, 659 problem, 606-607 and representative sets, 652 ex Central nodes in flow networks, 429 ex Central splitters in median-finding, 729-730 in Quicksort, 732 Certifiers, in efficient certification, 464 Chain molecules, entropy of, 547-550 ex Chandra, A. K., 551 Change detection in Segmented Least Squares Problem, 263
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