Date 14 Oct. 1991
Filter Results

Proceedings 32nd Annual Symposium on Foundations of Computer Science (Cat. No.91CH30627)
Publication Year: 1991 
A linear time algorithm for triconnectivity augmentation
Publication Year: 1991 , Page(s): 548  559
Cited by: Papers (4)The problem of finding the smallest set of edges whose addition triconnects an undirected graph is considered. This is a fundamental graphtheoretic problem that has applications in designing reliable networks and faulttolerant computing. A linear time sequential algorithm is given for the problem. This is a substantial improvement over the best previous algorithm for this problem, which runs in ... View full abstract»

Finding the hidden path: time bounds for allpairs shortest paths
Publication Year: 1991 , Page(s): 560  568
Cited by: Papers (6)  Patents (5)The allpairs shortest paths problem in weighted graphs is investigated. An algorithm called the hidden paths algorithm, which finds these paths in time O(m*+n n^{2} log n), where
m * is the number of edges participating in shortest paths, is presented. It is argued thatm * is likely to be small in practice, since m*=O(n log n) with high probability for many probability di... View full abstract» 
Search problems in the decision tree model
Publication Year: 1991 , Page(s): 576  585
Cited by: Patents (1)The relative power of determinism, randomness, and nondeterminism for search problems in the Boolean decision tree model is studied. It is shown that the CNF search problem is complete for all the variants of decision trees. It is then shown that the gaps between the nondeterministic, the randomized, and the deterministic complexities can be arbitrarily large for search problems. The special case ... View full abstract»

A quadratic time algorithm for the minmax length triangulation
Publication Year: 1991 , Page(s): 414  423
Cited by: Papers (2)  Patents (12)It is shown that a triangulation of a set of
n points in the plane that minimizes the maximum edge length can be computed in timeO (n ^{2}). The algorithm is reasonably easy to implement and is based on the theorem that there is a triangulation with minmax edge length that contains the relative neighborhood graph of the points as a subgraph. With minor modificatio... View full abstract» 
An approximation algorithm for the number of zeros or arbitrary polynomials over
Publication Year: 1991 , Page(s): 662  669GF [q ]
Cited by: Papers (1)The authors design the first polynomial time (for an arbitrary and fixed field
GF [q ]) (∈, δ)approximation algorithm for the number of zeros of arbitrary polynomialf (x _{1}. . .x _{n}) overGF [q ]. It gives the first efficient method for estimating the number of zeros and nonzeros of multivariate polynomials o... View full abstract» 
Computing planar intertwines
Publication Year: 1991 , Page(s): 802  811
Cited by: Papers (1)The proof of Wagner's conjecture by N. Robertson and P. Seymour gives a finite description of any family of graphs which is closed under the minor ordering, called the obstructions of the family. Since the intersection and the union of two minor closed graph families are again a minor closed graph family, an interesting question is that of computing the obstructions of the new family given the obs... View full abstract»

Reliable computation with noisy circuits and decision treesa general
Publication Year: 1991 , Page(s): 602  611n logn lower bound
Cited by: Papers (14)  Patents (1)Boolean circuits in which gates independently make errors with probability (at most) ε are considered. It is shown that the critical number crit(
f ) of a functionf yields lower bound Ω(crit(f ) log crit (f )) for the noisy circuit size. The lower bound is proved for an even stronger computational model, static Boolean decision trees with erroneous answe... View full abstract» 
Applications of a poset representation to edge connectivity and graph rigidity
Publication Year: 1991 , Page(s): 812  821
Cited by: Papers (10)A poset representation for a family of sets defined by a labeling algorithm is investigated. Poset representations are given for the family of minimum cuts of a graph, and it is shown how to compute them quickly. The representations are the starting point for algorithms that increase the edge connectivity of a graph, from λ to a given target τ=λ+δ, adding the fewest edges p... View full abstract»

Dynamic scheduling on parallel machines
Publication Year: 1991 , Page(s): 111  120
Cited by: Papers (1)The problem of online job scheduling on various parallel architectures is studied. An
O ((log logn )^{1/2 })competitive algorithm for online dynamic scheduling on ann ×n mesh is given. It is proved that this algorithm is optimal up to a constant factor. The algorithm is not greedy, and the lower bound proof shows that no greedylike algorithm can ... View full abstract» 
Competitive algorithms for layered graph traversal
Publication Year: 1991 , Page(s): 288  297
Cited by: Papers (4)A layered graph is a connected, weighted graph whose vertices are partitioned into sets
L _{0}={s },L _{1},L _{2}, . . ., and whose edges run between consecutive layers. Its width is max{L _{i}}. In the online layered graph traversal problem, a searcher starts ats in a layered graph of unknown width and tries to... View full abstract» 
Reporting points in halfspaces
Publication Year: 1991 , Page(s): 207  215The author considers the halfspace range reporting problem: Given a finite set
P of points inE ^{d}, preprocess it so that given a query halfspace γ, the points ofp ∩γ can be reported efficiently. It is shown that, with almost linear storage, this problem can be solved substantially more efficiently than the more general simplex range searching pr... View full abstract» 
Computing sums of radicals in polynomial time
Publication Year: 1991 , Page(s): 670  677
Cited by: Papers (2)For a certain sum of radicals the author presents a Monte Carlo algorithm that runs in polynomial time to decide whether the sum is contained in some number field
Q (α), and, if so, its coefficient representation inQ (α) is computed. As a special case the algorithm decides whether the sum is zero. The main algorithm is based on a subalgorithm which is of interest in it... View full abstract» 
A new characterization of Mehlhorn's polynomial time functionals
Publication Year: 1991 , Page(s): 342  347
Cited by: Papers (4)A. Cobham (1964) presented a machineindependent characterization of computational feasibility, via inductive definition. R. Constable (1973) was apparently the first to consider the notion of feasibility for type 2 functionals. K. Mehlhorn's (1976) study of feasible reducibilities proceeds from Constable's work. Here, a class of polytime operators is defined, using a generalization of Cobham's de... View full abstract»

Approximating clique is almost NPcomplete
Publication Year: 1991 , Page(s): 2  12
Cited by: Papers (58)The computational complexity of approximating ω(
G ), the size of the largest clique in a graphG , within a given factor is considered. It is shown that if certain approximation procedures exist, then EXPTIME=NEXPTIME and NP=P View full abstract» 
Approximate representation theory of finite groups
Publication Year: 1991 , Page(s): 733  742The asymptotic stability and complexity of floating point manipulation of representations of a finite group
G are considered, especially splitting them into irreducible constituents and deciding their equivalence. Using rapid mixing estimates for random walks, the authors analyze a classical algorithm by J. Dixon (1970). They find that both its stability and complexity critically depend o... View full abstract» 
How to learn an unknown environment
Publication Year: 1991 , Page(s): 298  303
Cited by: Papers (10)The authors consider the problem faced by a newborn that must explore and learn an unknown room with obstacles in it. They seek algorithms that achieve a bounded ratio of the worstcase distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map. The situation is complicated by the fact that the latter off... View full abstract»

Tree automata, mucalculus and determinacy
Publication Year: 1991 , Page(s): 368  377
Cited by: Papers (38)It is shown that the propositional mucalculus is equivalent in expressive power to finite automata on infinite trees. Since complementation is trivial in the mucalculus, the equivalence provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results. It is also shown how mucalculus c... View full abstract»

Communication complexity towards lower bounds on circuit depth
Publication Year: 1991 , Page(s): 249  257
Cited by: Papers (10)M. Karchmer et al. (1991) considered the circuit depth complexity of
n bit Boolean function constructed by composing up tod =logn /log logn levels ofk =logn bit Boolean functions. Any such function is in AC^{1}. They conjecture that circuit depth is additive under composition, which would imply that any (bounded fanin) circuit for ... View full abstract» 
Randomized multidimensional search trees: further results in dynamic sampling
Publication Year: 1991 , Page(s): 216  227
Cited by: Papers (5)The use of randomization in dynamic search structures by means of a technique called dynamic sampling is investigated. In particular, an efficient algorithm for dynamic (logarithmic time) point location in 3D partitions induced by a set of possibly interesting polygons in
R ^{3} is given. The expected running time of the algorithm on a random sequence of updates is close to optim... View full abstract» 
Simulating BPP using a general weak random source
Publication Year: 1991 , Page(s): 79  89
Cited by: Papers (23)  Patents (1)It is shown how to simulate BPP and approximation algorithms in polynomial time using the output from a δsource. A δsource is a weak random source that is asked only once for
R bits, and must output anR bit string according to some distribution that places probability no more than 2^{δR} on any particular string. Also given are two applications: one ... View full abstract» 
A theory of using history for equational systems with applications
Publication Year: 1991 , Page(s): 348  357A general theory of using a congruence closure based simplifier (CCNS) proposed by P. Chew (1980) for computing normal forms is developed, and several applications are presented. An independent set of postulates is given, and it is proved that CCNS can be used for any system that satisfies them. It is then shown that CCNS can be used for consistent convergent systems and for various kinds of prior... View full abstract»

Faster uniquely represented dictionaries
Publication Year: 1991 , Page(s): 642  649The authors present a solution to the dictionary problem where each subset of size
n of an ordered universe is represented by a unique structure, containing a (unique) binary search tree. The structure permits the execution of search, insert, and delete operations inO (n ^{1/3}) time in the worst case. They also give a general lower bound, stating that for any uni... View full abstract» 
Connected components in
Publication Year: 1991 , Page(s): 688  697O (lg^{3/2V}) parallel time for the CREW PRAM
Cited by: Papers (3)Computing the connected components of an undirected graph
G =(V ,E ) on V =n vertices and E  =m edges is addressed. An efficient and simple algorithm that runs inO (lg^{3/2}n ) time usingn +m CREW processors is presented View full abstract» 
Towards a theory of nearly constant time parallel algorithms
Publication Year: 1991 , Page(s): 698  710
Cited by: Papers (9)It is demonstrated that randomization is an extremely powerful tool for designing very fast and efficient parallel algorithms. Specifically, a running time of
O (lg*n ) (nearlyconstant), with high probability, is achieved usingn /lg*n (optimal speedup) processors for a wide range of fundamental problems. Also given is a constant time algorithm which, using ... View full abstract»