48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)最新文献_第2页

Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions 三维胖四面体并集的几乎紧界

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.9

Esther Ezra, M. Sharir

{"title":"Almost Tight Bound for the Union of Fat Tetrahedra in Three Dimensions","authors":"Esther Ezra, M. Sharir","doi":"10.1109/FOCS.2007.9","DOIUrl":"https://doi.org/10.1109/FOCS.2007.9","url":null,"abstract":"We show that the combinatorial complexity of the. union of n \"fat\" tetrahedra in 3-space (i.e., tetrahedra all of whose solid angles are at least .some fixed constant) of arbitrary sizes, is O(n2+epsiv),for any epsiv > 0: the bound is almost tight in the worst case, thus almost settling a conjecture of Pach el al. [24]. Our result extends, in a significant way, the result of Pach et al. [24] for the restricted case of nearly congruent cubes. The analysis uses cuttings, combined with the Dobkin-K'irkpatrick hierarchical decomposition of convex polytopes, in order to partition space into subcells, so that, on average, the overwhelming majority of the tetrahedra intersecting a subcell Delta behave as fat dihedral wedges in Delta. As an immediate corollary, we obtain that the combinatorial complexity of the union of n cubes in R3 having arbitrary side lengths, is O(n2+epsiv), for any epsiv > 0 again, significantly extending the result of [24]. Our analysis can easily he extended to yield a nearly-quadratic bound on the complexity of the union of arbitrarily oriented fat triangular prisms (whose cross-sections have, arbitrary sizes) in R3. Finally, we show that a simple variant of our analysis implies a nearly-linear bound on the complexity of the union of fat triangles in the plane.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126742119","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}

引用次数: 21

Inferring Local Homology from Sampled Stratified Spaces 从抽样分层空间推断局部同调

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.33

Paul Bendich, David Cohen-Steiner, Herbert Edelsbrunner, J. Harer, Dmitriy Morozov

引用次数: 14

Exponential Time/Space Speedups for Resolution and the PSPACE-completeness of Black-White Pebbling 黑白卵石的分辨率和pspace -完备性的指数时间/空间加速

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.22

Philipp Hertel, T. Pitassi

引用次数: 54

Covert Multi-Party Computation 隐蔽多方计算

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.21

Nishanth Chandran, Vipul Goyal, R. Ostrovsky, A. Sahai

引用次数: 27

Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits 深三电路中底部扇入的误差与功率

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.30

A. Chattopadhyay

{"title":"Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits","authors":"A. Chattopadhyay","doi":"10.1109/FOCS.2007.30","DOIUrl":"https://doi.org/10.1109/FOCS.2007.30","url":null,"abstract":"We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty 'number on the forehead' model. Our method is based on the notion of voting polynomial degree of functions and extends the degree-discrepancy lemma in the recent work of Sherstov (2007). Using this we prove that depth three circuits consisting of a MAJORITY gate at the output, gates computing arbitrary symmetric function at the second layer and arbitrary gates of bounded fan-in at the base layer i.e. circuits of type MAJ o SYMM o ANYO(1) cannot simulate the circuit class AC0 in sub-exponential size. Further, even if the fan-in of the bottom ANY gates are increased to o(log log n), such circuits cannot simulate AC0 in quasi-polynomial size. This is in contrast to the classical result of Yao and Beigel-Tarui that shows that such circuits, having only MAJORITY gales, can simulate the class ACC0 in quasi-polynomial size when the bottom fan-in is increased to poly-logarithmic size. In the second part, we simplify the arguments in the breakthrough work of Bourgain (2005) for obtaining exponentially small upper bounds on the correlation between the boolean function MODq and functions represented bv polynomials of small degree over Zm, when m,q ges 2 are co-prime integers. Our calculation also shows similarity with techniques used to estimate discrepancy of functions in the multiparty communication setting. This results in a slight improvement of the estimates of Bourgain et al. (2005). It is known that such estimates imply that circuits of type MAJ o MODm o ANDisin log n cannot compute the MODq function in sub-exponential size. It remains a major open question to determine if such circuits can simulate ACC0 in polynomial size when the bottom fan-in is increased to poly-logarithmic size.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124381000","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}

引用次数: 67

Derandomization of Sparse Cyclotomic Integer Zero Testing 稀疏分环整数零检验的非随机化

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.23

Qi Cheng

{"title":"Derandomization of Sparse Cyclotomic Integer Zero Testing","authors":"Qi Cheng","doi":"10.1109/FOCS.2007.23","DOIUrl":"https://doi.org/10.1109/FOCS.2007.23","url":null,"abstract":"The zero testing and sign determination problems of real algebraic numbers of high extension degree are important in computational complexity and numerical analysis. In this paper we concentrate an sparse cyclotomic integers. Given an integer n and a sparse polynomial f(x) = Ckxe(k) + ck-1xe(k-1) + ... + c1xe(1)over Z, we present a deterministic polynomial time algorithm to decide whether f(wn) is zero or not, where f(wn) denotes the n-th primitive root of unity e2piradic(-1/n). All previously known algorithms are either randomized, or do not run in polynomial time. As a side result, we prove that if n is free of prime factors less than k + 1, there exist k field automorphisms sigma1, sigma2, ... , sigmak in the Galois group Gal (Q(wn)/Q) such that for any nonzero integers c1, c2 ... , ck and for any integers 0 les e1 < e2 < ... < ek < n, there exists i so that |sigmai(ckwn ek + ck-1wn e(k-1) + ... + c1wn e(1)) | ges 1/2(k(2)log n+klogk).","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123275880","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}

引用次数: 31

Local Global Tradeoffs in Metric Embeddings 度量嵌入中的局部全局权衡

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1137/070712080

M. Charikar, K. Makarychev, Yury Makarychev

引用次数: 41

On the Advantage over Random for Maximum Acyclic Subgraph 论最大无环子图优于随机的优点

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.47

M. Charikar, K. Makarychev, Yury Makarychev

引用次数: 29

Hardness of Reconstructing Multivariate Polynomials over Finite Fields 有限域上多元多项式重构的硬度

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1137/070705258

Parikshit Gopalan, Subhash Khot, Rishi Saket

{"title":"Hardness of Reconstructing Multivariate Polynomials over Finite Fields","authors":"Parikshit Gopalan, Subhash Khot, Rishi Saket","doi":"10.1137/070705258","DOIUrl":"https://doi.org/10.1137/070705258","url":null,"abstract":"We study the polynomial reconstruction problem, for low-degree multivariate polynomials over F[2]. In this problem, we are given a set of points x epsi {0, 1}n and target values f(x) epsi {0, 1} for each of these points, with the promise that there is a polynomial over F[2] of degree at most d that agrees with f at 1 - epsiv fraction of the points. Our goal is to find agree d polynomial that has good-agreement with f. We show that it is NP-hard to find a polynomial that agrees with f on more than 1 - 2-d + delta fraction of the points for any epsiv, delta > 0. This holds even with the stronger promise that the polynomial that fits the data is in fact linear, wherejis the algorithm is allowed to find a polynomial of degree d. Previously the only known, hardness of approximation (or even NP-completeness) was for the case when d = I, which follows from a celebrated result of Has tad. In the setting of computational learning, our result shows the hardness of (non-proper) agnostic learning of parities, where the learner is allowed, a low-degree polynomial over F[2] as a hypothesis. This is the first non-proper hardness result for this central problem in computational learning. Our results extend-to multivariate polynomial reconstruction over any finite field.","PeriodicalId":197431,"journal":{"name":"48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128699180","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}

引用次数: 88

Approximate Hypergraph Partitioning and Applications 近似超图划分及其应用

48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07) Pub Date : 2007-10-21 DOI: 10.1109/FOCS.2007.11

E. Fischer, A. Matsliah, A. Shapira

引用次数: 39