Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)最新文献

{"title":"A tight characterization of NP with 3 query PCPs","authors":"V. Guruswami, D. Lewin, M. Sudan, L. Trevisan","doi":"10.1109/SFCS.1998.743424","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743424","url":null,"abstract":"It is known that there exists a PCP characterization of NP where the verifier makes 3 queries and has a one-sided error that is bounded away from 1; and also that 2 queries do not suffice for such a characterization. Thus PCPs with 3 queries possess non-trivial verification power and motivate the task of determining the lowest error that can be achieved with a 3-query PCP. Recently, Hastad (1997) has shown a tight characterization of NP by constructing a 3-query PCP verifier with \"error\" arbitrarily close to 1/2. Unfortunately this verifier makes two-sided error and Hastad makes essential use of this feature. One-sided error, on the other hand, is a natural notion to associate with a proof system, since it has the desirable property that every rejected proof has a short counterexample. The question of determining the smallest error for which there exists a 3-query PCP verifier making one-sided error and accepting an NP-complete language, however, remained open. We resolve this question by showing that NP has a 3-query PCP with a one-sided error that is arbitrarily close to 1/2. This characterization is tight, i.e., the error cannot be lower. This result is in seeming contradiction with the results of Trevisan (1997) and Zwick (1998) who show that in order to recognize an NP-complete language, the error probability of a PCP verifier making 3 non-adaptive queries and having one-sided error must be at least 5/8. We get around this bottleneck by designing an adaptive 3-query PCP for NP. Our result yields the first tight analysis of an adaptive PCP; and reveals a previously unsuspected separation between the powers of adaptive and non-adaptive PCPs. Our design and analysis of adaptive PCPs can be extended to higher number of queries as well and we give an example of such a proof system with 5 queries. Our adaptive verifiers yield proof systems whose error probabilities match those of previous constructions, while also achieving one-sidedness in the error. This raises new questions about the power of adaptive PCPs, which deserve further study.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132520683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"All pairs shortest paths in weighted directed graphs-exact and almost exact algorithms","authors":"Uri Zwick","doi":"10.1109/SFCS.1998.743464","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743464","url":null,"abstract":"We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in O/spl tilde/(n/sup 2+/spl mu//) time, where /spl mu/ satisfies the equation /spl omega/(1,/spl mu/,1)=1+2/spl mu/ and /spl omega/(1,/spl mu/,1) is the exponent of the multiplication of an n/spl times/n/sup /spl mu// matrix by an n/sup /spl mu///spl times/n matrix. The currently best available bounds on /spl omega/(1,/spl mu/,1), obtained by Coppersmith and Winograd, and by Huang and Pan, imply that /spl mu/<0.575. The running time of our algorithm is therefore O(n/sup 2.575/). Our algorithm improves on the O/spl tilde/(n/sup (3+/spl omega/)/2/) time algorithm, where /spl omega/=/spl omega/(1,1,1)<2.376 is the usual exponent of matrix multiplication, obtained by Alon, Galil and Margalit, whose running time is only known to be O(n/sup 2.688/). The second algorithm solves the APSP problem almost exactly for directed graphs with arbitrary non-negative real weights. The algorithm runs in O/spl tilde/((n/sup /spl omega////spl epsiv/)/spl middot/log(W//spl epsiv/)) time, where /spl epsiv/>0 is an error parameter and W is the largest edge weight in the graph, after the edge weights are scaled so that the smallest non-zero edge weight in the graph is 1. It returns estimates of all the distances in the graph with a stretch of at most 1+/spl epsiv/. Corresponding paths can also be found efficiently.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123333729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The finite capacity dial-a-ride problem","authors":"M. Charikar, B. Raghavachari","doi":"10.1109/SFCS.1998.743496","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743496","url":null,"abstract":"We give the first non-trivial approximation algorithm for the Capacitated Dial-a-Ride problem: given a collection of objects located at points in a metric space, a specified destination point for each object, and a vehicle with a capacity of at most k objects, the goal is to compute a shortest tour for the vehicle in which all objects can be delivered to their destinations while ensuring that the vehicle carries at most k objects at any point in time. The problem is known under several names, including the Stacker Crane problem and the Dial-a-Ride problem. No theoretical approximation guarantees were known for this problem other than for the cases k=1, /spl infin/ and the trivial O(k) approximation for general capacity k. We give an algorithm with approximation ratio O(/spl radic/k) for special instances on a class of tree metrics called height-balanced trees. Using Bartal's recent results on the probabilistic approximation of metric spaces by tree metrics, we obtain an approximation ratio of O(/spl radic/k log n log log n) for arbitrary n point metric spaces. When the points lie on a line (line metric), we provide a 2-approximation algorithm. We also consider the Dial-a-Ride problem in another framework: when the vehicle is allowed to leave objects at intermediate locations and pick them up at a later time and deliver them. For this model, we design an approximation algorithm whose performance ratio is O(1) for tree metrics and O(log n log log n) for arbitrary metrics. We also study the ratio between the values of the optimal solutions for the two versions of the problem. We show that unlike in k-delivery TSP in which all the objects are identical, this ratio is not bounded by a constant for the Dial-a-Ride problem, and it could be as large as R(k/sup 2/3/).","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126219269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolutionary trees can be learned in polynomial time in the two-state general Markov model","authors":"Mary Cryan, L. A. Goldberg, P. Goldberg","doi":"10.1109/SFCS.1998.743494","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743494","url":null,"abstract":"The j-State General Markov Model of evolution M. Steel (1994) is a stochastic model concerned with the evolution of strings over an alphabet of size j. In particular, the Two-State General Markov Model of evolution generalises the well-known Cavender-Farris-Neyman model of evolution by removing the symmetry restriction (which requires that the probability that a '0'' turns into a '1' along an edge is the same as the probability that a '1' turns into a '0' along the edge). M. Farach and S. Kannan (1996) showed how to PAC-learn Markov Evolutionary Trees in the Cavender-Farris-Neyman model provided that the target tree satisfies the additional restriction that all pairs of leaves have a sufficiently high probability of being the same. We show how to remove both restrictions and thereby obtain the first polynomial-time PAC-learning algorithm (in the sense of Kearns et al.) for the general class of Two-State Markov Evolutionary Trees.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116669847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oblivious transfer with a memory-bounded receiver","authors":"C. Cachin, C. Crépeau, Julien Marcil","doi":"10.1109/SFCS.1998.743500","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743500","url":null,"abstract":"We propose a protocol for oblivious transfer that is unconditionally secure under the sole assumption that the memory size of the receiver is bounded. The model assumes that a random bit string slightly larger than the receiver's memory is broadcast (either by the sender or by a third party). In our construction, both parties need memory of size in /spl theta/(n/sup 2-2/spl alpha//) for some /spl alpha/< 1/2 , when a random string of size N=n/sup 2-/spl alpha/-/spl beta// is broadcast, for /spl alpha/>/spl beta/>0, whereas a malicious receiver can have up to /spl gamma/N bits of memory for any /spl gamma/<1. In the course of our analysis, we provide a direct study of an interactive hashing protocol closely related to that of M. Naor et al. (1998).","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122619241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A linguistic characterization of bounded oracle computation and probabilistic polynomial time","authors":"John C. Mitchell, Mark Mitchell, A. Scedrov","doi":"10.1109/SFCS.1998.743523","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743523","url":null,"abstract":"We present a higher-order functional notation for polynomial-time computation with an arbitrary 0, 1-valued oracle. This formulation provides a linguistic characterization for classes such as NP and BPP, as well as a notation for probabilistic polynomial-time functions. The language is derived from Hofmann's adaptation of Bellantoni-Cook safe recursion, extended to oracle computation via work derived from that of Kapron and Cook. Like Hofmann's language, ours is an applied typed lambda calculus with complexity bounds enforced by a type system. The type system uses a modal operator to distinguish between two sorts of numerical expressions. Recursion can take place on only one of these sorts. The proof that the language captures precisely oracle polynomial time is model-theoretic, using adaptations of various techniques from category theory.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132245358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recommendation systems: a probabilistic analysis","authors":"Ravi Kumar, P. Raghavan, S. Rajagopalan, A. Tomkins","doi":"10.1109/SFCS.1998.743517","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743517","url":null,"abstract":"A recommendation system tracks past actions of a group of users to make recommendations to individual members of the group. The growth of computer-mediated marketing and commerce has led to increased interest in such systems. We introduce a simple analytical framework for recommendation systems, including a basis for defining the utility of such a system. We perform probabilistic analyses of algorithmic methods within this framework. These analyses yield insights into how much utility can be derived from the memory of past actions and on how this memory can be exploited.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114500641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A TDI system and its application to approximation algorithms","authors":"M. Cai, Xiaotie Deng, Wenan Zang","doi":"10.1109/SFCS.1998.743448","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743448","url":null,"abstract":"We obtain a necessary and sufficient condition for tournaments to possess a min-max relation on packing and covering directed cycles, together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem in this class of tournaments; the condition and the algorithms are all based on a totally dual integral (TDI) system, a theoretical framework introduced by J. Edmonds and R. Giles (1994) for establishing min-max results. As a consequence, we find a 2.5-approximation polynomial time algorithm for the feedback vertex set problem in any tournament.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"579 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116067495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semidefinite relaxations for parallel machine scheduling","authors":"M. Skutella","doi":"10.1109/SFCS.1998.743498","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743498","url":null,"abstract":"We consider the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time of jobs. Whereas the best previously known approximation algorithms for this problem are based on LP relaxations, we give a 3/2-approximation algorithm that relies on a convex quadratic programming relaxation. For the special case of two machines we present a further improvement to a 1.2752-approximation; we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by M.X. Goemans and D.P. Williamson (1995) for the MAXCUT problem and its refined version of U. Feige and M.X. Goemans (1995). To the best of our knowledge, this is the first time that convex and semidefinite programming techniques (apart from LPs) are used in the area of scheduling.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"07 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127289382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Which problems have strongly exponential complexity?","authors":"R. Impagliazzo, R. Paturi, F. Zane","doi":"10.1109/SFCS.1998.743516","DOIUrl":"https://doi.org/10.1109/SFCS.1998.743516","url":null,"abstract":"For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper we address the relative likelihood of sub-exponential algorithms for these problems. We introduce a generalized reduction which we call sub-exponential reduction family (SERF) that preserves sub-exponential complexity. We show that Circuit-SAT is SERF-complete for all NP-search problems, and that for any fixed k, k-SAT, k-Colorability, k-Set Cover Independent Set, Clique, Vertex Cover are SERF-complete for the class SNP of search problems expressible by second order existential formulas whose first order part is universal. In particular, sub-exponential complexity for any one of the above problems implies the same for all others. We also look at the issue of proving strongly exponential lower bounds (that is, bounds of the form 2/sup /spl Omega/(n)/) for AC/sup 0/. This problem is even open far depth-3 circuits. In fact, such a bound for depth-3 circuits with even limited (at most n/sup /spl epsiv//) fan-infer bottom-level gates would imply a nonlinear size lower bound for logarithmic depth circuits. We show that with high probability even degree 2 random GF(2) polynomials require strongly exponential site for /spl Sigma//sub 3//sup k/ circuits for k=o(loglogn). We thus exhibit a much smaller space of 2(0(/sup n2/)) functions such that almost every function in this class requires strongly exponential size /spl Sigma//sub 3//sup k/ circuits. As a corollary, we derive a pseudorandom generator (requiring O(n/sup 2/) bits of advice) that maps n bits into a larger number of bits so that computing parity on the range is hard for /spl Sigma//sub 3//sup k/ circuits. Our main technical lemma is an algorithm that, for any fixed /spl epsiv/>0, represents an arbitrary k-CNF formula as a disjunction of 2/sup /spl epsiv/n/ k-CNF formulas that are sparse, e.g., each having O(n) clauses.","PeriodicalId":228145,"journal":{"name":"Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1998-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126081251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}