Date 2729 Oct. 1986
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[Front cover]
Publication Year: 1986, Page(s): C1 PDF (153 KB) 
Table of contents
Publication Year: 1986, Page(s):xi  xiv PDF (397 KB) 

Machtey Award
Publication Year: 1986, Page(s): v PDF (20 KB) 
An O(n2(m + n log n) log n) mincost flow algorithm
Publication Year: 1986, Page(s):1  9The minimumcost flow problem is the following: given a network with n vertices and m edges, find a maximum flow of minimum cost. Many network problems are easily reducible to this problem. A polynomialtime algorithm for the problem has been known for some time [EK], but only recently a strongly polynomial algorithm was discovered [Ts]. In this paper we design an O(n2(m + n log n)log n) algorithm... View full abstract»

Probabilistic construction of deterministic algorithms: Approximating packing integer programs
Publication Year: 1986, Page(s):10  18
Cited by: Papers (11)We consider the problem of approximating an integer program by first solving its relaxation linear program and "rounding" the resulting solution. For several packing problems, we prove probabilistically that there exists an integer solution close to the optimum of the relaxation solution. We then develop a methodology for converting such a probabilistic existence proof to a deterministic approxima... View full abstract»

On a search problem related to branchandbound procedures
Publication Year: 1986, Page(s):19  28
Cited by: Papers (2) 
Probabilistic Boolean decision trees and the complexity of evaluating game trees
Publication Year: 1986, Page(s):29  38
Cited by: Papers (24)The Boolean Decision tree model is perhaps the simplest model that computes Boolean functions; it charges only for reading an input variable. We study the power of randomness (vs. both determinism and nondeterminism) in this model, and prove separation results between the three complexity measures. These results are obtained via general and efficient methods for computing upper and lower bounds o... View full abstract»

A physical interpretation of graph connectivity, and its algorithmic applications
Publication Year: 1986, Page(s):39  48
Cited by: Papers (3) 
The asymptotic spectrum of tensors and the exponent of matrix multiplication
Publication Year: 1986, Page(s):49  54
Cited by: Papers (4)We introduce an asymptotic data structure for the relative bilinear complexity of bilinear maps (tensors). It consists of a compact Hausdorff space Δ together with an interpretation of the tensors under consideration as continuous functions on Δ. The asymptotic rank of a tensor is simply the maximum of the associated function. On the way we present a new method for estimating the exp... View full abstract»

Storing a dynamic sparse table
Publication Year: 1986, Page(s):55  60
Cited by: Papers (4)We present a family of data structures that can process a sequence of insert, delete, and lookup instructions such that each lookup and deletion is done in constant worstcase time and each insertion is done in constant expected time. The amount of space used by each data structure is proportional to the maximal number of elements that need to be stored at any moment in time. View full abstract»

Lower bounds for accessing binary search trees with rotations
Publication Year: 1986, Page(s):61  70We describe two methods for obtaining lower bounds on the cost of accessing a sequence of nodes of a symmetrically ordered binary search tree, where rotations can be done on the tree. The bounds apply to offline as well as online algorithms. View full abstract»

What search algorithm gives optimal averagecase performance when search resources are highly limited?
Publication Year: 1986, Page(s):71  76This paper presents a probabilistic model for studying the question: given n search resources, where in the search tree should they be expended? Specifically, a leastcost roottoleaf path is sought in a random tree. The tree is known to be binary and complete to depth N. Arc costs are independently set either to 1 (with probability p)or to 0 (with probability lp). The cost of a leaf is the sum ... View full abstract»

Geometric applications of DavenportSchinzel sequences
Publication Year: 1986, Page(s):77  86
Cited by: Papers (4)We present efficient algorithms for the following geometric problems: (i) Preprocessing of a 2D polyhedral terrain so as to support fast ray shooting queries from a fixed point. (ii) Determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations. (iii) Determining whether a given convex polygon can be translated and rotated so as to f... View full abstract»

Lower bounds on the complexity of multidimensional searching
Publication Year: 1986, Page(s):87  96
Cited by: Papers (3)We establish new lower bounds on the complexity of several searching problems. We show that the time for solving the partial sum problem on n points in d dimensions is at least proportional to (log n/log 2m/n)d1 in both the worst and average cases; m denotes the amount of storage used. This bound is provably tight for m = Ω(nlogcn) and any c ≫ d 1. We also prove a lower bound of &#... View full abstract»

Planar realizations of nonlinear DavenportSchinzel sequences by segments
Publication Year: 1986, Page(s):97  106
Cited by: Papers (2)Let G={l1,...,ln} be a collection of n segments in the plane, none of which is vertical. Viewing them as the graphs of partially defined linear functions of x, let YG be their lower envelope (i.e. pointwise minimum). YG is a piecewise linear function, whose graph consists of subsegments of the segments lt. Hart and Sharir [HS] have shown that YG consists of at most O(nα(n)) segments (where ... View full abstract»

Proving by example and gap theorems
Publication Year: 1986, Page(s):107  116
Cited by: Papers (3)This paper proposes a proving_by_example method, which works as follows: Given a geometry proposition we can easily present a concrete numerical example such that in order to determine whether the proposition is generally true, one need only to try this example up to a certain number of significant digits. This is an application of a recently discovered gap theorem. View full abstract»

An optimal algorithm for the allnearestneighbors problem
Publication Year: 1986, Page(s):117  122
Cited by: Papers (3)Given a set V of n points in kdimensional space, and an Lqmetric (Minkowski metric), the AllNearestNeighbors problem is defined as follows: For each point p in V, find all those points in V{p} that are closest to p under the distance metric Lq. We give an O(nlogn) algorithm for the AllNearestNeighbors problem, for fixed dimension k and fixed metric Lq. Since there is an Ω(n logn) low... View full abstract»

An algorithm for constructing the aspect graph
Publication Year: 1986, Page(s):123  131
Cited by: Papers (19)In this paper we present tight bounds on the maximum size of aspect graphs and give worstcase optimal algorithms for their construction, first in the convex case and then in the general case. In particular, we give upper and lower bounds on the maximum size (including vertex labels) of Θ(n3) and Θ(n5) and algorithms for constructing the aspect graph which run in time O(n3) and O(n5) ... View full abstract»

An algorithmic approach to the automated design of parts orienters
Publication Year: 1986, Page(s):132  142
Cited by: Papers (4)This paper concerns the design of parts orienters  the dual to the motion planning problem. Two particular paradigms are considered and their abstractions to the computational domain lead to interesting problems in graph pebbling and function composition on finite sets. Polynomial time algorithms are developed for the abstracted problems. View full abstract»

Finiteresolution computational geometry
Publication Year: 1986, Page(s):143  152
Cited by: Papers (14)  Patents (4)Geometric algorithms are usually designed with continuous parameters in mind. When the underlying geometric space is intrinsically discrete, as is the case for computer graphics problems, such algorithms are apt to give invalid solutions if properties of a finiteresolution space are not taken into account. In this paper we discuss an approach for transforming geometric concepts and algorithms fro... View full abstract»

On Newton's method for polynomials
Publication Year: 1986, Page(s):153  161
Cited by: Papers (1)Let Pd be the set of polynomials over the complex numbers of degree d with all its roots in the unit ball. For f ∈ Pd, let Γf be the set of points for which Newton's method converges to a root, and let Af ≡ Γf ∩ B2(O)/B2(O), i.e. the density of Γf in the ball of radius 2. For each d we consider Ad, the worstcase density Af for f ∈ Pd. In S... View full abstract»

How to generate and exchange secrets
Publication Year: 1986, Page(s):162  167
Cited by: Papers (277)  Patents (20)In this paper we introduce a new tool for controlling the knowledge transfer process in cryptographic protocol design. It is applied to solve a general class of problems which include most of the twoparty cryptographic problems in the literature. Specifically, we show how two parties A and B can interactively generate a random integer N = pÂ¿q such that its secret, i.e., the prime factors (p, q),... View full abstract»

Information theoretic reductions among disclosure problems
Publication Year: 1986, Page(s):168  173
Cited by: Papers (21)Alice disposes of some number of secrets. She is willing to disclose one of them to Bob. Although she agrees to let him choose which secret he wants, she is not willing to allow him to gain any information on more than one secret. On the other hand, Bob does not want Alice to know which secret he wishes. An allornothing disclosure is one by which, as soon as Bob has gained any information whatso... View full abstract»

Proofs that yield nothing but their validity and a methodology of cryptographic protocol design
Publication Year: 1986, Page(s):174  187
Cited by: Papers (38)  Patents (21)In this paper we demonstrate the generality and wide applicability of zeroknowledge proofs, a notion introduced by Goldwasser, Micali and Rackoff. These are probabilistic and interactive proofs that, for the members x of a language L, efficiently demonstrate membership in the language without conveying any additional knowledge. So far, zeroknowledge proofs were known only for some number theoret... View full abstract»