Abstract
A pervasive theme in Compute Science (as in any science or for that matter in life) is tradeoffs. This is, of course, a recurring theme in many of Ian Munro’s papers (e.g. in data structures, streaming algorithms). In one form or another, time space tradeoffs can be found in many settings. Another traditional research area concerns tradeoffs between performance (e.g. approximation bounds) vs complexity bounds. Newer areas of research consider various issues of tradeoffs involving concepts relating to fairness, privacy, conceptual simplicity, robustness, and self-interest (e.g. truthfulness). We will review some of the well established results as well as some of the many open questions involving tradeoffs.
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References
Ada, A., Chattopadhyay, A., Cook, S.A., Fontes, L., Koucký, M., Pitassi, T.: The hardness of being private. In: IEEE Conference on Computational Complexity, pp. 192–202 (2012)
Agarwal, M., Kayal, N., Saxena, N.: Primes is in p. Annals of Mathematics 160(r21), 781–793 (2004)
Ajtai, M.: A non-linear time lower bound for boolean branching programs. Theory of Computing 1(1), 149–176 (2005)
Alekhnovich, M., Borodin, A., Buresh-Oppenheim, J., Impagliazzo, R., Magen, A.: Toward a model for backtracking and dynamic programming. Electronic Colloquium on Computational Complexity (ECCC) 16, 38 (2009)
Alon, N., Matias, Y., Szegedy, M.: The space complexity of approximating the frequency moments. J. Comput. Syst. Sci. 58(1), 137–147 (1999)
Alt, H., Mehlhorn, K., Munro, J.I.: Partial match retrieval in implicit data structures. Inf. Process. Lett. 19(2), 61–65 (1984)
Andrew, L.L.H., Lin, M., Wierman, A.: Optimality, fairness, and robustness in speed scaling designs. In: SIGMETRICS, pp. 37–48 (2010)
Attiya, H., Welch, J.: Distributed Computing: Fundamentals, Simulations, and Advanced Topics. Wiley Series on Parallel and Distributed Computing. Wiley (2004)
Barkol, O., Rabani, Y.: Tighter lower bounds for nearest neighbor search and related problems in the cell probe model. J. Comput. Syst. Sci. 64(4), 873–896 (2002)
Beame, P.: A general sequential time-space tradeoff for finding unique elements. In: STOC, pp. 197–203 (1989)
Beame, P., Beck, C., Impagliazzo, R.: Time-space tradeoffs in resolution: superpolynomial lower bounds for superlinear space. In: STOC, pp. 213–232 (2012)
Beame, P., Vee, E.: Time-space tradeoffs, multiparty communication complexity, and nearest-neighbor problems. In: IEEE Conference on Computational Complexity, p. 18 (2002)
Beck, C., Nordstrom, J., Tang, B.: Some trade-off results for the polynomial calculus. In: STOC (2013)
Blum, M., Floyd, R.W., Pratt, V.R., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. J. Comput. Syst. Sci. 7(4), 448–461 (1973)
Borodin, A., Cook, S.A.: A time-space tradeoff for sorting on a general sequential model of computation. SIAM J. Comput. 11(2), 287–297 (1982)
Borodin, A., Fich, F.E., Meyer auf der Heide, F., Upfal, E., Wigderson, A.: A time-space tradeoff for element distinctness. SIAM J. Comput. 16(1), 97–99 (1987)
Borodin, A., Fich, F.E., Meyer auf der Heide, F., Upfal, E., Wigderson, A.: A tradeoff between search and update time for the implicit dictionary problem. Theor. Comput. Sci. 58, 57–68 (1988)
Borodin, A., Fischer, M.J., Kirkpatrick, D.G., Lynch, N.A., Tompa, M.: A time-space tradeoff for sorting on non-oblivious machines. J. Comput. Syst. Sci. 22(3), 351–364 (1981)
Borodin, A., Ostrovsky, R., Rabani, Y.: Lower bounds for high dimensional nearest neighbor search and related problems. In: Discrete and Computational Geometry – The Goodman-Polack Festschrift, vol. 25, pp. 255–276 (2003)
Brodsky, A., Fich, F.E.: Efficient synchronous snapshots. In: PODC, pp. 70–79 (2004)
Brönnimann, H., Chan, T.M., Chen, E.Y.: Towards in-place geometric algorithms and data structures. In: Symposium on Computational Geometry, pp. 239–246 (2004)
Buresh-Oppenheim, J., Davis, S., Impagliazzo, R.: A stronger model of dynamic programming algorithms. Algorithmica 60(4), 938–968 (2011)
Buss, S.R., Williams, R.: Limits on alternation-trading proofs for time-space lower bounds. In: IEEE Conference on Computational Complexity, pp. 181–191 (2012)
Canetti, R., Goldreich, O.: Bounds on tradeoffs between randomness and communication complexity. Computational Complexity 3, 141–167 (1993)
Carlsson, S., Munro, J.I., Poblete, P.V.: An implicit binomial queue with constant insertion time. In: Karlsson, R., Lingas, A. (eds.) SWAT 1988. LNCS, vol. 318, pp. 1–13. Springer, Heidelberg (1988)
Carrascal, J., Riederer, C., Erramilli, V., Cherubini, M., de Oliveira, R.: Your browsinf behavior for a big mac: Economics of personal information online. In: WWW (2013)
Chakrabarti, A., Chazelle, B., Gum, B., Lvov, A.: A lower bound on the complexity of approximate nearest-neighbor searching on the hamming cube. In: STOC, pp. 305–311 (1999)
Chan, T.: Comparison-based time-space lower bounds for selection. ACM Transaction on Algorithms 6(n) (2010)
Chandra, A.K., Furst, M.L., Lipton, R.J.: Multi-party protocols. In: STOC, pp. 94–99 (1983)
Cobham, A.: The recognition problem for the set of perfect squares. In: SWAT (FOCS), pp. 78–87 (1966)
Cook, S.A., Reckhow, R.A.: The relative efficiency of propositional proof systems. J. Symb. Log. 44(1), 36–50 (1979)
Datar, M., Gionis, A., Indyk, P., Motwani, R.: Maintaining stream statistics over sliding windows. SIAM J. Comput. 31(6), 1794–1813 (2002)
Demaine, E.D., López-Ortiz, A., Munro, J.I.: Frequency estimation of internet packet streams with limited space. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 348–360. Springer, Heidelberg (2002)
Dolev, D., Strong, H.R.: Authenticated algorithms for byzantine agreement. SIAM J. Comput. 12(4), 656–666 (1983)
Downey, R.G., Fellows, M.R.: Parameterized Complexity, 530 p. Springer (1999)
Dubey, P.: Inefficiency of nash equilibrium. Mathematics of Operations Research 11(1), 1–8 (1986)
Duris, P., Galil, Z.: A time-space tradeoff for language recognition. Mathematical Systems Theory 17(1), 3–12 (1984)
Duris, P., Galil, Z., Schnitger, G.: Lower bounds on communication complexity. Inf. Comput. 73(1), 1–22 (1987)
Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006)
Feigenbaum, J., Jaggard, A.D., Schapira, M.: Approximate privacy: foundations and quantification (extended abstract). In: Proceedings of the 11th ACM Conference on Electronic Commerce, EC 2010, pp. 167–178. ACM (2010)
Feldman, M., Meir, R., Tennenholtz, M.: Stability scores: measuring coalitional stability. In: AAMAS, pp. 771–778 (2012)
Fich, F.E., Miltersen, P.B.: Tables should be sorted (on random access machines). In: Sack, J.-R., Akl, S.G., Dehne, F., Santoro, N. (eds.) WADS 1995. LNCS, vol. 955, pp. 482–493. Springer, Heidelberg (1995)
Fich, F.E., Ruppert, E.: Hundreds of impossibility results for distributed computing. Distributed Computing 16(2-3), 121–163 (2003)
Fischer, M.J., Lynch, N.A.: A lower bound for the time to assure interactive consistency. Inf. Process. Lett. 14(4), 183–186 (1982)
Fortnow, L.: Time-space tradeoffs for satisfiability. J. Comput. Syst. Sci. 60(2), 337–353 (2000)
Franceschini, G., Grossi, R., Munro, J.I., Pagli, L.: Implicit b-trees: a new data structure for the dictionary problem. J. Comput. Syst. Sci. 68(4), 788–807 (2004)
Franceschini, G., Munro, J.I.: Implicit dictionaries with o(1) modifications per update and fast search. In: SODA, pp. 404–413 (2006)
Frederickson, G.N.: Implicit data structures for the dictionary problem. J. ACM 30(1), 80–94 (1983)
Frederickson, G.N.: Upper bounds for time-space trade-offs in sorting and selection. J. Comput. Syst. Sci. 34(1), 19–26 (1987)
Gál, A., Miltersen, P.B.: The cell probe complexity of succinct data structures. Theor. Comput. Sci. 379(3), 405–417 (2007)
Gibson, D., Kleinberg, J.M., Raghavan, P.: Clustering categorical data: An approach based on dynamical systems. VLDB J. 8(3-4), 222–236 (2000)
Golab, L., DeHaan, D., Demaine, E.D., López-Ortiz, A., Munro, J.I.: Identifying frequent items in sliding windows over on-line packet streams. In: Internet Measurement Comference, pp. 173–178 (2003)
Halstenberg, B., Reischuk, R.: Different modes of communication. SIAM J. Comput. 22(5), 913–934 (1993)
Huynh, T., Nordström, J.: On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity. In: STOC, pp. 233–248 (2012)
Hyafil, L.: On the parallel evaluation of multivariate polynomials. SIAM J. Comput. 8(2), 120–123 (1979)
Impagliazzo, R., Wigderson, A.: P = BPP if e requires exponential circuits: Derandomizing the xor lemma. In: STOC, pp. 220–229 (1997)
Impagliazzo, R., Williams, R.: Communication complexity with synchronized clocks. In: IEEE Conference on Computational Complexity, pp. 259–269 (2010)
Indyk, P., Motwani, R.: Approximate nearest neighbors: Towards removing the curse of dimensionality. In: STOC, pp. 604–613 (1998)
Kaelbling, L.P., Littman, M.L., Moore, A.W.: Reinforcement learning: A survey. J. Artif. Intell. Res. (JAIR) 4, 237–285 (1996)
Karchmer, M.: Two time-space tradeoffs for element distinctness. Theor. Comput. Sci. 47(3), 237–246 (1986)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. Computer Science Review 3(2), 65–69 (2009)
Krizanc, D., Peleg, D., Upfal, E.: A time-randomness tradeoff for oblivious routing (extended abstract). In: STOC, pp. 93–102 (1988)
Kushilevitz, E.: Privacy and communication complexity. SIAM J. Discrete Math. 5(2), 273–284 (1992)
Kushilevitz, E., Ostrovsky, R., Rabani, Y.: Efficient search for approximate nearest neighbor in high dimensional spaces. SIAM J. Comput. 30(2), 457–474 (2000)
Lin, M., Wierman, A., Roytman, A., Meyerson, A., Andrew, L.L.H.: Online optimization with switching cost. SIGMETRICS Performance Evaluation Review 40(3), 98–100 (2012)
McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: FOCS, pp. 94–103 (2007)
Munro, J.I.: An implicit data structure supporting insertion, deletion, and search in o(log2 n) time. J. Comput. Syst. Sci. 33(1), 66–74 (1986)
Munro, J.I., Paterson, M.: Optimal algorithms for parallel polynomial evaluation. J. Comput. Syst. Sci. 7(2), 189–198 (1973)
Munro, J.I., Paterson, M.: Selection and sorting with limited storage. Theor. Comput. Sci. 12, 315–323 (1980)
Munro, J.I., Poblete, P.V.: Searchability in merging and implicit data structures. BIT 27(3), 324–329 (1987)
Munro, J.I., Raman, V.: Selection from read-only memory and sorting with minimum data movement. Theor. Comput. Sci. 165(2), 311–323 (1996)
Munro, J.I., Suwanda, H.: Implicit data structures for fast search and update. J. Comput. Syst. Sci. 21(2), 236–250 (1980)
Muthukrishnan, S.: Theory of data stream computing: where to go. In: PODS, pp. 317–319 (2011)
Nepomnnjaščiǐ, V.: Rudimentary predicates and turing computations. Dokl. Akad. Nauk SSSR 195, 282–284 (1070); English translation in Soviet Math. Dokl. 11, 1462–1465 (1970)
Nisan, N., Ronen, A.: Algorithmic mechanism design. Games and Economic Behavior 35(1-2), 166–196 (2001)
Nisan, N., Wigderson, A.: Rounds in communication complexity revisited. SIAM J. Comput. 22(1), 211–219 (1993)
Nordstrom, J.: Pebble games, proof complexity, and time-space trade-offs. In: Logical Methods in Computer Science (to appear, 2013)
Papadimitriou, C.H., Schapira, M., Singer, Y.: On the hardness of being truthful. In: FOCS, pp. 250–259 (2008)
Papadimitriou, C.H., Sipser, M.: Communication complexity. J. Comput. Syst. Sci. 28(2), 260–269 (1984)
Pease, M.C., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)
Peleg, D., Upfal, E.: A trade-off between space and efficiency for routing tables. J. ACM 36(3), 510–530 (1989)
Pippenger, N.: On simultaneous resource bounds (preliminary version). In: FOCS, pp. 307–311 (1979)
Rabin, M.O.: Probabilistic algorithm for testing primality. Journal of Number Theory 12(1), 128–138 (1980)
Radhakrishnan, J., Raman, V.: A tradeoff between search and update in dictionaries. Inf. Process. Lett. 80(5), 243–247 (2001)
Raman, V., Ramnath, S.: Improved upper bounds for time-space trade-offs for selection. Nord. J. Comput. 6(2), 162–180 (1999)
Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)
Savitch, W.J.: Deterministic simulation of non-deterministic turing machines (detailed abstract). In: STOC, pp. 247–248 (1969)
Solovay, R., Strassen, V.: Erratum: A fast monte-carlo test for primality. SIAM J. Comput. 7(1), 118 (1978)
Valiant, L.G., Skyum, S., Berkowitz, S., Rackoff, C.: Fast parallel computation of polynomials using few processors. SIAM J. Comput. 12(4), 641–644 (1983)
Vazirani, V.V.: Approximation algorithms. Springer-Verlag New York, Inc., New York (2001)
Williams, R.: Alternation-trading proofs, linear programming, and lower bounds. In: STACS, pp. 669–680 (2010)
Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press (2011)
Yao, A.C.-C.: Some complexity questions related to distributive computing (preliminary report). In: STOC, pp. 209–213 (1979)
Yao, A.C.-C.: Near-optimal time-space tradeoff for element distinctness. SIAM J. Comput. 23(5), 966–975 (1994)
Yao, F.F., Demers, A.J., Shenker, S.: A scheduling model for reduced cpu energy. In: FOCS, pp. 374–382 (1995)
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Borodin, A. (2013). Computing (and Life) Is All about Tradeoffs. In: Brodnik, A., López-Ortiz, A., Raman, V., Viola, A. (eds) Space-Efficient Data Structures, Streams, and Algorithms. Lecture Notes in Computer Science, vol 8066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40273-9_9
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