Jonathan F. Buss

Pattern matching for permutations

Given a permutation T of 1 to n, and a permutation P of 1 to k, for k ≤ n, we wish to find a k-element subsequence of T whose elements are ordered according to the permutation P. For example, if P is (1,2,..., k), then we wish to find an increasing subsequence of length k in T; this special case can be done in time O(n log log n) [CW]. We prove that the general problem is NP-complete. We give a polynomial time algorithm for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3,1,4,2) nor its reverse, the subpattern (2,4,1,3).

Parallel Algorithms with Processor Failures and Delays

We study efficient deterministic parallel algorithms on two models: restartable fail-stop CRCW PRAMs and asynchronous PRAMs. In the first model, synchronous processes are subject to arbitrary stop failures and restarts determined by an on-line adversary and involving loss of private but not shared memory; the complexity measures arecompleted work(where processors are charged for completed fixed-size update cycles) andoverhead ratio(completed work amortized over necessary work and failures). In the second model, the result of the computation is a serialization of the actions of the processors determined by an on-line adversary; the complexity measure istotal work(number of steps taken by all processors). Despite their differences, the two models share key algorithmic techniques. We present new algorithms for theWrite-Allproblem (in whichPprocessors write ones into an array of sizeN) for the two models. These algorithms can be used to implement a simulation strategy for anyNprocessor PRAM on a restartable fail-stopPprocessor CRCW PRAM such that it guarantees a terminating execution of each simulatedNprocessor step, withO(log2N) overhead ratio, andO(min{N+Plog2N+MlogN,N·P0.59}) (subquadratic) completed work (whereMis the number of failures during this steps simulation). This strategy has a range of optimality. We also show that theWrite-AllrequiresN+?(PlogP) completed/total work on these models forP?N.

A sublinear space, polynomial time algorithm for directed s-t connectivity

A deterministic sublinear space, polynomial-time algorithm for directed s-t connectivity, which is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph, is presented. For n-vertex graphs, the algorithm can use as little as n/2/sup Theta /( square root log n) space while still running in polynomial time.<<ETX>>

Pattern Matching for Permutations

Given a permutation T of 1 to n, and a permutation P of 1 to k, for k ≤ n, we wish to find a k-element subsequence of T whose elements are ordered according to the permutation P. For example, if P is (1,2,..., k), then we wish to find an increasing subsequence of length k in T; this special case can be done in time O(n log log n) [CW]. We prove that the general problem is NP-complete. We give a polynomial time algorithm for the decision problem, and the corresponding counting problem, in the case that P is separable—i.e. contains neither the subpattern (3,1,4,2) nor its reverse, the subpattern (2,4,1,3).

A Sublinear Space, Polynomial Time Algorithm for Directed s - t Connectivity

Directed s-t connectivity is the problem of detecting whether there is a path from vertex s to vertex t in a directed graph. We present the first known deterministic sublinear space, polynomial time algorithm for directed s-t connectivity. For

Lower Bounds on Universal Traversal Sequences Based on Chains of Length Five

n

Nondeterminism within P

-vertex graphs, our algorithm can use as little as

Simplifying the weft hierarchy

n/2^{\Theta(\sqrt{\log n})}

The computational complexity of some problems of linear algebra

space while still running in polynomial time.

Algorithms in the W-Hierarchy

Universal traversal sequences for cycles require length ?(n1.43), improving the previous bound of ?(n1.33). For d ? 3, universal traversal sequences for d-regular graphs require length ?(d0.57n2.43). For constant d, the best previous bound was ?(n2.33).