The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completeness results are so measure-independent and could lead to their generalization to this wider and more invariant class of measures. It also demonstrates a sharp difference between recently discovered pseudorandom strings and the objects known before.<>
{"title":"Homogeneous measures and polynomial time invariants","authors":"L. Levin","doi":"10.1109/SFCS.1988.21919","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21919","url":null,"abstract":"The usual probability distributions are concentrated on strings that do not differ noticeably in any fundamental characteristics, except their informational size (Kolmogorov complexity). The formalization of this statement is given and shown to distinguish a class of homogeneous probability measures suggesting various applications. In particular, it could explain why the average case NP-completeness results are so measure-independent and could lead to their generalization to this wider and more invariant class of measures. It also demonstrates a sharp difference between recently discovered pseudorandom strings and the objects known before.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132708373","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}
The packet-routing problem is examined in a network-independent context. The goal is to devise a strategy for routing that works well for a wide variety of networks. To achieve this goal, the routing problem is partitioned into two stages: a path-selection stage and a scheduling stage. In the first stage, paths for the packets are found with small maximum distance and small maximum congestion. Once the paths are fixed, both are lower bounds on the time required to deliver the packets. In the second stage, a schedule is found for the movement of each packet along its path so that no two packets traverse the same edge at the same time and the total time and maximum queue size required to route all of the packets to their destinations are minimized. The second stage is more challenging and is the focus of this study.<>
{"title":"Universal packet routing algorithms","authors":"F. Leighton, B. Maggs, Satish Rao","doi":"10.1109/SFCS.1988.21942","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21942","url":null,"abstract":"The packet-routing problem is examined in a network-independent context. The goal is to devise a strategy for routing that works well for a wide variety of networks. To achieve this goal, the routing problem is partitioned into two stages: a path-selection stage and a scheduling stage. In the first stage, paths for the packets are found with small maximum distance and small maximum congestion. Once the paths are fixed, both are lower bounds on the time required to deliver the packets. In the second stage, a schedule is found for the movement of each packet along its path so that no two packets traverse the same edge at the same time and the total time and maximum queue size required to route all of the packets to their destinations are minimized. The second stage is more challenging and is the focus of this study.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124595066","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}
The authors present the first optimal algorithm for the following problem: given n line segments in the plane, compute all k pairwise intersections in O(n log n+k) time. Within the same asymptotic cost the algorithm will also compute the adjacencies of the planar subdivision induced by the segments, which is a useful data structure for contour-filling on raster devices.<>
{"title":"An optimal algorithm for intersecting line segments in the plane","authors":"B. Chazelle, H. Edelsbrunner","doi":"10.1145/147508.147511","DOIUrl":"https://doi.org/10.1145/147508.147511","url":null,"abstract":"The authors present the first optimal algorithm for the following problem: given n line segments in the plane, compute all k pairwise intersections in O(n log n+k) time. Within the same asymptotic cost the algorithm will also compute the adjacencies of the planar subdivision induced by the segments, which is a useful data structure for contour-filling on raster devices.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122028699","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}
A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudorandom sequences. Combining this construction with other arguments, a number of consequences are obtained.<>
{"title":"Hardness vs. randomness","authors":"N. Nisan, A. Wigderson","doi":"10.1109/SFCS.1988.21916","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21916","url":null,"abstract":"A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudorandom sequences. Combining this construction with other arguments, a number of consequences are obtained.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129642281","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}
Pseudorandom generators are known to exist, assuming the existence of functions that cannot be efficiently inverted on the distributions induced by applying the function iteratively polynomially many times. This sufficient condition is also necessary, but it is difficult to check whether particular functions, assumed to be one-way, are also one-way on their iterates. This raises the fundamental question of whether the mere existence of one-way functions suffices for the construction of pseudorandom generators. Progress toward resolving this question is presented. Regular functions in which every image of a k-bit string has the same number of preimages of length k are considered. It is shown that if a regular function is one-way, then pseudorandom generators do exist. In particular, assuming the intractability of general factoring, it can be proved that the pseudorandom generators do exist. Another application is the construction of a pseudorandom generator based on the assumed intractability of decoding random linear codes.<>
{"title":"On the existence of pseudorandom generators","authors":"Oded Goldreich, H. Krawczyk, M. Luby","doi":"10.1109/SFCS.1988.21917","DOIUrl":"https://doi.org/10.1109/SFCS.1988.21917","url":null,"abstract":"Pseudorandom generators are known to exist, assuming the existence of functions that cannot be efficiently inverted on the distributions induced by applying the function iteratively polynomially many times. This sufficient condition is also necessary, but it is difficult to check whether particular functions, assumed to be one-way, are also one-way on their iterates. This raises the fundamental question of whether the mere existence of one-way functions suffices for the construction of pseudorandom generators. Progress toward resolving this question is presented. Regular functions in which every image of a k-bit string has the same number of preimages of length k are considered. It is shown that if a regular function is one-way, then pseudorandom generators do exist. In particular, assuming the intractability of general factoring, it can be proved that the pseudorandom generators do exist. Another application is the construction of a pseudorandom generator based on the assumed intractability of decoding random linear codes.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115278730","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}
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