2426 Oct. 1988
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29th Annual Symposium on Foundations of Computer Science (IEEE Cat. No.88CH26526)
Publication Year: 1988 PDF (251 KB) 
Results on learnability and the VapnikChervonenkis dimension
Publication Year: 1988, Page(s):120  129
Cited by: Papers (3)The problem of learning a concept from examples in a distributionfree model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite VapnikChervonenkis (VC) dimension. An important variation on the probl... View full abstract»

On the complexity of kinodynamic planning
Publication Year: 1988, Page(s):306  316
Cited by: Papers (37)The following problem, is considered: given a robot system find a minimaltime trajectory from a start position and velocity to a goal position and velocity, while avoiding obstacles and respecting dynamic constraints on velocity and acceleration. The simplified case of a point mass under Newtonian mechanics together with velocity and acceleration bounds is considered. The point must be flown from... View full abstract»

Speeding up dynamic programming
Publication Year: 1988, Page(s):488  496
Cited by: Papers (4)A number of important computational problems in molecular biology, geology, speech recognition, and other areas can be expressed as recurrences which have typically been solved with dynamic programming. By using more sophisticated data structures, and by taking advantage of further structure from the applications, the authors speed up the computation of several of these recurrences by one or two o... View full abstract»

Bounds on the cover time
Publication Year: 1988, Page(s):479  487
Cited by: Papers (4)A particle that moves on a connected unidirected graph G with n vertices is considered. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph, starting from a given vertex. Upper and lower bounds are presented that relate the expected ... View full abstract»

Take a walk, grow a tree
Publication Year: 1988, Page(s):469  478
Cited by: Papers (5)A simple randomized algorithm is presented for maintaining dynamically evolving binary trees on hypercube networks. The algorithm guarantees that: (1) nodes adjacent in the tree are within distance O(log log N) in an Nprocessor hypercube, and (2) with overwhelming probability, no hypercube processor is assigned more than O(1+M/N) tree nodes, where M is... View full abstract»

Dynamic networks are as fast as static networks
Publication Year: 1988, Page(s):206  219
Cited by: Papers (13)An efficient simulation is given to show that dynamic networks are as fast as static ones up to a constant multiplicative factor. That is, any task can be performed in a dynamic asynchronous network essentially as fast as in a static synchronous network. The simulation protocol is based on an approach in which locality is perceived as the key to fast adaptation to changes in network topology. The ... View full abstract»

A faster PSPACE algorithm for deciding the existential theory of the reals
Publication Year: 1988, Page(s):291  295
Cited by: Papers (7)The decision problem for the existential theory of the reals is the problem of deciding if the set {x∈Rn ; P(x) is nonempty, where P(x) is a predicate which is a Boolean function of atomic predicates either of which is a Boolean function of atomic predicates either of the form fi(x)⩾0 or f View full abstract»

Genus
Publication Year: 1988, Page(s):458  468g graphs have pagenumber O(√g )A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus g has pagenumber O(√g); and (2) most nver... View full abstract»

Parallel comparison algorithms for approximation problems
Publication Year: 1988, Page(s):194  203The authors consider that they have n elements from a totally ordered domain and are allowed to perform p parallel comparisons in each time unit (round). They determine, up to a constant factor, the time complexity of several approximation problems in the common parallel comparison tree model of L.G. Valiant, for all admissible values of n, p, and ε, where ... View full abstract»

New algorithms for finding irreducible polynomials over finite fields
Publication Year: 1988, Page(s):283  290
Cited by: Papers (12)  Patents (5)An algorithm is presented for finding an irreducible polynomial of specified degree over a finite field. It is deterministic and runs in polynomial time for fields of small characteristics. A proof is given of the stronger result, that the problem of finding irreducible polynomials of specified degree over a finite field K is deterministicpolynomialtime reducible to the problem of facto... View full abstract»

A Las Vegas algorithm for linear programming when the dimension is small
Publication Year: 1988, Page(s):452  456
Cited by: Papers (13)  Patents (1)An algorithm for solving linear programming problems is given. The expected number of arithmetic operations required by the algorithm is given. The expectation is with respect to the random choices made by the algorithm, and the bound holds for any given input. The technique can be extended to other convex programming problems View full abstract»

The complexity of the pigeonhole principle
Publication Year: 1988, Page(s):346  355
Cited by: Papers (19)The pigeonhole principle for n is the statement that there is no onetoone function between a set of size n and a set of size n1. This statement can be formulated as an unlimitedfanin constant depth polynomialsize Boolean formula PHPn in n(n1) variables, PHPn can be proved in the propositional calculus; that is, a sequence of... View full abstract»

Optimal parallel algorithm for the Hamiltonian cycle problem on dense graphs
Publication Year: 1988, Page(s):186  193
Cited by: Papers (1)G.A. Dirac's classical theorem (1952) asserts that if every vertex of a graph G on n vertices has degree at least n /2, the G has a Hamiltonian cycle. A fast parallel algorithm on a concurrentreadexclusivewrite parallel randomaccess machine (CREW PRAM) is given to find a Hamiltonian cycle in such graphs. The algorithm uses a linear number of processors and i... View full abstract»

Fast management of permutation groups
Publication Year: 1988, Page(s):272  282
Cited by: Papers (5)Novel algorithms for computation in permutation groups are presented. They provide an orderofmagnitude improvement in the worstcase analysis of the basic permutationgroup problems, including membership testing and computing the order of the group. For deeper questions about the group, including finding composition factors, an improvement of up to four orders of magnitude is realized. These and... View full abstract»

Polynomial algorithm for the
Publication Year: 1988, Page(s):444  451k cut problem
Cited by: Papers (28)  Patents (3)The
k cut problem is to find a partition of an edge weighted graph intok nonempty components, such that the total edge weight between components is minimum. This problem is NPcomplete for arbitraryk and its version involving fixing a vertex in each component is NP hard even fork =3. A polynomial algorithm for the case of a fixedk is presented View full abstract» 
On the existence of pseudorandom generators
Publication Year: 1988, Page(s):12  24
Cited by: Papers (10)  Patents (1)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 oneway, are also oneway on their iterates. This raises the fundamental qu... View full abstract»

Verifying temporal properties of finitestate probabilistic programs
Publication Year: 1988, Page(s):338  345
Cited by: Papers (18)The complexity of testing whether a finitestate (sequential or concurrent) probabilistic program satisfies its specification expressed in linear temporal logic. For sequential programs an exponentialtime algorithm is given and it is shown that the problem is in PSPACE; this improves the previous upper bound by two exponentials and matches the known lower bound. For concurrent programs is is show... View full abstract»

Combinatorial complexity bounds for arrangements of curves and surfaces
Publication Year: 1988, Page(s):568  579
Cited by: Papers (9)The authors study both the incidence counting and the manyfaces problem for various kinds of curves, including lines, pseudolines, unit circles, general circles, and pseudocircles. They also extend the analysis to three dimensions, where they concentrate on the case of spheres, which is relevant for the threedimensional unitdistance problem. They obtain upper bounds for certain quantities. The ... View full abstract»

Sublineartime parallel algorithms for matching and related problems
Publication Year: 1988, Page(s):174  185
Cited by: Papers (11)The authors present the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. The results are based on a better understanding of the combinatorial structure of the above problems, which lead to new algorithmic techniques. In particular, it is shown how t... View full abstract»

On the effects of feedback in dynamic network protocols
Publication Year: 1988, Page(s):231  245
Cited by: Papers (3)A framework is introduced that provides a unified way for proving correctness as well as analyzing performance of a class of communication protocols called (asynchronous) reset protocols. They are logarithmic transformers, converting protocols working in a static asynchronous network into protocols working in a dynamic asynchronous network. The design of reset protocols is a classical problem in c... View full abstract»

Homogeneous measures and polynomial time invariants
Publication Year: 1988, Page(s):36  41
Cited by: Papers (4)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 NPcompletene... View full abstract»

Universal packet routing algorithms
Publication Year: 1988, Page(s):256  269
Cited by: Papers (29)The packetrouting problem is examined in a networkindependent 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 pathselection stage and a scheduling stage. In the first stage, paths for the packets are found with small maximum distance and small maximum congestion. Onc... View full abstract»

Lattices, mobius functions and communications complexity
Publication Year: 1988, Page(s):81  90
Cited by: Papers (12)A general framework for the study of a broad class of communication problems is developed. It is based on a recent analysis of the communication complexity of graph connectivity. The approach makes use of combinatorial lattice theory View full abstract»

Combinatorial algorithms for the generalized circulation problem
Publication Year: 1988, Page(s):432  443
Cited by: Papers (6)  Patents (1)A generalization of the maximumflow problem is considered in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e)λ(e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exc... View full abstract»