23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)最新文献

{"title":"The complexity of compacting hierarchically specified layouts of integrated circuits","authors":"Thomas Lengauer","doi":"10.1109/SFCS.1982.92","DOIUrl":"https://doi.org/10.1109/SFCS.1982.92","url":null,"abstract":"In many CAD systems for VLSI design the specification of a layout is internally represented by a set of geometric constraints that take the form of linear inequalities between pairs of layout components. Some of the constraints may be explicitly stated by the circuit designer. Others are internally generated by the CAD system, using the design rules of the fabrication process. Layout compaction is then equivalent to finding a minimum area layout satisfying all constraints. We discuss the complexity of the constraint resolution problem arising in this context. Hereby we allow circuits to be specified hierarchically. The complexity of the constraint resolution is then measured in terms of the length of the hierarchical specification. We show the following results: 1. It is decidable in polynomial (cubic) time whether a given hierarchical layout specification yields a consistent set of geometric constraints. The size of minimum area layouts satisfying the constraints can also be determined in cubic time. 2. For every layout specification that is consistent a hierarchical description L of a minimum area layout can be computed in polynomial time in the length of L. 3. There is a consistent layout specification with the following property: No layout satisfying the constraints is concise, i.e., every hierarchical layout description consistent with the specification has a length which grows exponentially in the length of the specification. 4. We define a subclass of so-called well-formed layout specifications. Each well-formed specification has a concise layout, which can be hierarchically described in linear space. Such a layout can be found in polynomial time. However, it is in general not a minimum area layout. Indeed, there is a consistent well-formed specification all of whose minimum area layouts are inconcise,.i.e., need exponential space to be described.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115927956","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":"Storing a sparse table with O(1) worst case access time","authors":"M. Fredman, J. Komlos, E. Szemerédi","doi":"10.1145/828.1884","DOIUrl":"https://doi.org/10.1145/828.1884","url":null,"abstract":"We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time. Both the data structure and the query algorithm are easy to implement.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116941664","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":"Parallel algorithms for minimum cuts and maximum flows in planar networks","authors":"Donald B. Johnson, S. M. Venkatesan","doi":"10.1145/31846.31849","DOIUrl":"https://doi.org/10.1145/31846.31849","url":null,"abstract":"Algorithms are given that compute maximum flows in planar directed networks either in O((logn)3) parallel time using O(n4) processors or O((logn)2) parallel time using O(n6) processors. The resource consumption of these algorithms is dominated by the cost of finding the value of a maximum flow. When such a value is given, or when the computation is on an undirected network, the bound is O((logn)2) time using O(n4) processors. No efficient parallel algorithm is known for the maximum flow problem in general networks.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124656713","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":"Generalised symmetries of polynomials in algebraic complexity","authors":"Carl Sturtivant","doi":"10.1109/SFCS.1982.70","DOIUrl":"https://doi.org/10.1109/SFCS.1982.70","url":null,"abstract":"Suppose a polynomial P(x), (where x is the column matrix of the indeterminates x1.~.x), has a symmetry analogous to those of the de~ermiRant, whereby taking a certain linear combination of the The purpose of the paper is to define the set of symmetries of a polynomial, explore its structure, and identify the computationally useful members; a method of computing the latter symmetries is presented. It is shown how the set of symmetries determines whether or not Gaussian style elimination or transformation style algorithms can aid computation. To this end a robust notion of the \"dimen-sion\" of a polynomial is defined, yielding a tech~ nique for proving negative results in complexity. Let ~'¥.. and z be n x 1 column matrices. z is the wrappeg convolution of ~ and ¥.. iff '1j z. = LX. Y.. d • z is the Hademard J i=l ~ ~+J mo n product (or pairwise product) of ~ and ¥..\"iff '1j z. = x. • y j • An efficient technique for eval-J J uating a wrapped convolution [1 p.254] relies upon transforming the convolution into a Hademard product by means of the discrete \"Fburier transform. The question \"can the permanent be transformed analogously in a way that may assist faster computation?\" is considered, and answered in part. In order to construct such a scheme whereby P can be evaluated at any point ~, it must be possible for the symmetry (T, t) to depend upon x, in order to introduce zeros into Tx + t. (In practice several successive transformations may be made, introducing successively more zeros whilst preserving those previously present. Such a scheme constitutes a Gaussian elimination style algorithm for evaluating P) • In order for this to be possible, it is necessary that some of the symmetries of P form a continuum: these continuous symmetries include all of the computationally useful symmetries of P. variables before evaluating P only alters the result by a constant factor plus a constant additive term, (where T is an n x n matrix of constants, t is an n X 1 matrix of constants and k,k' are constants) • Then P could be computed at ~ by computing P at Ta + t, multiplying by k and adding k'. If Ta + t has more components equal to zero than a then there may be some computational advantage in this scheme as compared to evaluating …","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132843656","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":"'Eventual' is earlier than 'immediate'","authors":"D. Dolev, R. Reischuk, H. Strong","doi":"10.1109/SFCS.1982.51","DOIUrl":"https://doi.org/10.1109/SFCS.1982.51","url":null,"abstract":"Two different notions of Byzantine Agreement - immediate and eventually - are defined depending on whether the agreement involves an action to be performed synchronously or not. The lower bounds for time complexity depend on what kind of agreement has to be achieved. All previous algorithms to reach Byzantine Agreement ensure immediate agreement. We present two algorithms that in many cases reach the second type of agreement faster than previously known algorithms showing that there actually is a difference between the two notions: Eventual Byzantine Agreement can be reached earlier than Immediate.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123128877","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 ellipsoid algorithm for linear inequalities in exact arithmetic","authors":"S. Ursic","doi":"10.1109/SFCS.1982.44","DOIUrl":"https://doi.org/10.1109/SFCS.1982.44","url":null,"abstract":"A modification of the ellipsoid algorithm is shown to be capable of testing for satisfiability a system of linear equations and inequalities with integer coefficients of the form Ax = b, x ≥ 0. All the rational arithmetic is performed exactly, without losing polynomiality of the computing time. In case of satisfiability, the approach always provides a rational feasible point. The bulk of the computations consists of a sequence of linear least squares problems, each a rank one modification of the preceding one. The continued fractions jump is used to compute some of the coordinates of a feasible point.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122258515","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":"Substitution of bounded rational cone","authors":"J. Beauquier, M. Latteux","doi":"10.1109/SFCS.1982.90","DOIUrl":"https://doi.org/10.1109/SFCS.1982.90","url":null,"abstract":"We study the family S of rational cones obtained by iterated substitutions from rational cones L1, .., Ln. This family is a semi-group and to every non empty word u defined on the alphabet {L1, ..., Ln}, corresponds a rational cone U of S. We give sufficient conditions for S to be free (U = U′ implies u = u′) and to verify the subpattern property (U ⊂ U′ implies u is a subpattern of u′). We study, more particularly, the case where L1, ..., Ln are bounded rational cones.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116712602","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":"An O(n3 log n) deterministic and an O (n 3) probabilistic isomorphism test for trivalent graphs","authors":"Z. Galil, C. Hoffmann, E. Luks, C. Schnorr, M. Weber","doi":"10.1109/SFCS.1982.62","DOIUrl":"https://doi.org/10.1109/SFCS.1982.62","url":null,"abstract":"The main results of this paper are an O(n3) probabilistic algorithm and an O(n3 log n) deterministic algorithm that test whether two given trivalent graphs are isomorphic. In fact, the algorithms construct the set of all isomorphisms of the two graphs. Variants of these algorithms construct the set of all automorphisms of a trivalent graph. The algorithms make use of some new improved permutation group algorithms that exploit the fact that the groups involved are 2-groups. A remarkable property of the probabilistic algorithm is that it computes Isoe,ei(X,Y), i = 1,...,m, m = O(n) (the set of all isomorhisms φ: X → Y with φ(e)=ei) for the cost of computing the single set Isoe,el(X,Y).","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124763441","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":"How to generate cryptographically strong sequences of pseudo random bits","authors":"M. Blum, S. Micali","doi":"10.1109/SFCS.1982.72","DOIUrl":"https://doi.org/10.1109/SFCS.1982.72","url":null,"abstract":"Much effort has been devoted in the second half of this century to make precise the notion of Randomness. Let us informally recall one of these definitions due to Kolmogorov []. A sequence of bits A =all a2••.•• at is random if the length of the minimal program outputting A is at least k We remark that the above definition is highly non constructive and rules out the possibility of pseudo random number generators. Also. the length of a program, from a Complexity Theory point of view, is a rather unnatural measure. A more operative definition of Randomness should be pursued in the light of modern Complexity Theory.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"129 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134290692","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":"Three applications of Kolmogorov-complexity","authors":"Stefan Reisch, G. Schnitger","doi":"10.1109/SFCS.1982.96","DOIUrl":"https://doi.org/10.1109/SFCS.1982.96","url":null,"abstract":"Kolmogorov-CoMplexity has turned out to be a very useful tool in proving lower bounds [5], [6], [7]. Here we will give further applications of Kolmogorov-Complexity. Firstly we will greatly simplify two well-known lower bound proofs: (a) the n(n logn/loglog n) lower bound for on-line-multiplication, originally proven in [2], [4], (b) the n(n 2 /log n) lower bound for a time-space trade-off in sorting [9]. We will also improve this bound to n(N 2 loglog N/log N). Secondly we will demonstrate how to use Kolmogorov-Complexity in analysing proba-bilistic algorithms: (c) We analyse in an elementary way the routing algorithm for n-dimensional cubes given in [10]. 1. The concept of Kolmogorov-Complexity Let C be the class of one-dimensional Turing-machines with tape-alphabet {O,I,B}. Let U be an universal machine in C. For w 1 ,w 2 E{O,I}* define the Kolmogorov-Complexity [3] by: K(w 1 {W 2 }: =the length of the shortest o/ 1 s t r i ng (\" pro gram I' J p, s uc h t hat U with input pBw2 computes wI and stops. K(w): =K(wlempty string). 45 Because one program p can only generate one word w, we have Fact I : Let w 2 E{O,l}* , then i) *{wl E{O,1}*IK(w 1 IW 2) ~n} <2 n + 1 _1 i i) (Especially) there exists a string w E{O,l}n with K(wlw 2) ~n If K(wl the empty string) =n , then w i s called a random string. Two easy consequences of Fact 1 are Fact 2: (Strings with low complexity are improbable). Let w 2 E{O,l}* be fixed and determine wI E{O,l}n by tossinq a fair coin n times, then for all c Fact 3: (Random strings are locally n almost random). Let w =w 1 w 2 w 3 E{O,l} be random. Then, with w'w 2 : =w 1 w 3 ' We need the following notation. For w: =w 1 w 1 w 2 w2\"\" ,w n w n Ol ·","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124042151","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}