26th Annual Symposium on Foundations of Computer Science (sfcs 1985)最新文献_第5页

An application of simultaneous approximation in combinatorial optimization 同时逼近在组合优化中的应用

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.8

A. Frank, É. Tardos

引用次数: 21

Amplification of probabilistic boolean formulas 概率布尔公式的放大

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.5

R. Boppana

引用次数: 62

On networks of noisy gates 在噪声门的网络上

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.41

N. Pippenger

引用次数: 189

Three theorems on polynomial degrees of NP-sets 关于np集多项式度的三个定理

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.61

K. Ambos-Spies

引用次数: 6

The complexity of parallel sorting 并行排序的复杂性

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1137/0216008

F. Heide, A. Wigderson

引用次数: 54

Robin hood hashing 罗宾汉哈希

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.48

P. Celis, P. Larson, J. Munro

引用次数: 119

The complexity of facets resolved 复杂的面解决了

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.56

C. Papadimitriou, David Wolfe

引用次数: 226

Motion planning in the presence of moving obstacles 存在移动障碍物时的运动规划

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1145/179812.179911

J. Reif, M. Sharir

{"title":"Motion planning in the presence of moving obstacles","authors":"J. Reif, M. Sharir","doi":"10.1145/179812.179911","DOIUrl":"https://doi.org/10.1145/179812.179911","url":null,"abstract":"This paper investigates the computational complexity of planning the motion of a body B in 2-D or 3-D space, so as to avoid collision with moving obstacles of known, easily computed, trajectories. Dynamic movement problems are of fundamental importance to robotics, but their computational complexity has not previously been investigated. We provide evidence that the 3-D dynamic movement problem is intractable even if B has only a constant number of degrees of freedom of movement. In particular, we prove the problem is PSPACE-hard if B is given a velocity modulus bound on its movements and is NP hard even if B has no velocity modulus bound, where in both cases B has 6 degrees of freedom. To prove these results we use a unique method of simulation of a Turing machine which uses time to encode configurations (whereas previous lower bound proofs in robotics used the system position to encode configurations and so required unbounded number of degrees of freedom). We also investigate a natural class of dynamic problems which we call asteroid avoidance problems: B, the object we wish to move, is a convex polyhedron which is free to move by translation with bounded velocity modulus, and the polyhedral obstacles have known translational trajectories but cannot rotate. This problem has many applications to robot, automobile, and aircraft collision avoidance. Our main positive results are polynomial time algorithms for the 2-D asteroid avoidance problem with bounded number of obstacles as well as single exponential time and nO(log n) space algorithms for the 3-D asteroid avoidance problem with an unbounded number of obstacles. Our techniques for solving these asteroid avoidance problems are novel in the sense that they are completely unrelated to previous algorithms for planning movement in the case of static obstacles. We also give some additional positive results for various other dynamic movers problems, and in particular give polynomial time algorithms for the case in which B has no velocity bounds and the movements of obstacles are algebraic in space-time.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132826238","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: 339

Computing ears and branchings in parallel 并行计算耳和分支

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.16

L. Lovász

引用次数: 68

Fast and efficient algorithms for sequential and parallel evaluation of polynomial zeros and of matrix polynomials 快速有效的顺序和并行求多项式零和矩阵多项式的算法

26th Annual Symposium on Foundations of Computer Science (sfcs 1985) Pub Date : 1985-10-21 DOI: 10.1109/SFCS.1985.25

V. Pan

{"title":"Fast and efficient algorithms for sequential and parallel evaluation of polynomial zeros and of matrix polynomials","authors":"V. Pan","doi":"10.1109/SFCS.1985.25","DOIUrl":"https://doi.org/10.1109/SFCS.1985.25","url":null,"abstract":"We evaluate all the real and complex zeros λ1,...,λn of an n-th degree univariate polynomial with the relative precision 1/2nc for a given positive constant c. If for all g,h, log |λg/λh-1| ≥ 1/2O(n) unless λg = λh, then we need O(n3log2n) arithmetic operations or O(n2log n) steps, n log n processors. O(n2log n) operations or O(n log n) parallel steps, n processors suffice if either all the zeros are real or for all g,h either |λg| = |λh| or 2O(n) ≥ (|λg/λh| - 1)| ≥ 1/2O(n). If all the zeros are either multiple or form complex conjugate pairs or if their moduli pairwise differ by the factors at least 1+1/nO(1), then O(n log2n) operations or O(log2n) steps, n processors suffice. Replacing 1+1/nO(1) above by 1+1/nO(loghn) for a positive h only requires to increase the time-complexity bounds by the factor loghn. Some of the presented algorithms extend Graeffe's method, other algorithms use the power sum techniques and the companion matrix computation; the latter ones are related to Bernoulli's and Leverrier's methods and to the power method and are extended in this paper to the evaluation of a matrix polynomial u(X) of degree N, (X is an n×n matrix), using O(N log N+n2.496) arithmetic operations. Such evaluation can be performed using O(log N+log2n) parallel steps, Nn+n3.496 processors or alternatively O(log2(nN)) steps, N/log N+n3.496 processors over arbitrary field of constants. Over rational constants, for almost all matrices X the number of processors can be reduced to Nn+n2.933 or to N/log N+n2.933, respectively; the bounds can be further reduced to O(log N+log2n)steps, N+n2.933 processors if u(X) is to be computed with a fixed arbitrarily high precision rather than exactly. For integer and well-conditioned matrices, the exponent 2.933 above can be decreased to 2.496. The results substantially improve the previously known upper estimates for the complexity of sequential and parallel evaluation of polynomial zeros and of matrix polynomials.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134368581","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: 12