The subclass of directed series-parallel graphs plays an important role in computer science. Whether a given graph is series-parallel is a well studied problem in algorithmic graph theory, for which fast sequential and parallel algorithms have been ...

We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system consisting of N disks d₁, d₂,...,d_N...

We propose a new solution for the fully dynamic single source shortest paths problem in a directed graph G = (N, A) with arbitrary arc weights, that works for any digraph and has optimal space requirements and query time. If a negative-length cycle is ...

We present a deterministic parallel algorithm that solves a n-dimensional system Ax=b of linear equations over an ordered field or over a subfield of the complex numbers. This algorithm uses O(log2n) parallel time and O(max{M(n),n2(loglogn)/logn}) ...

We consider a parallel tree contraction scheme which in each contraction phase removes leaves and nodes in the maximal chains. Let T(n) and P(n) denote the time and processor complexity required to compute the all nearest smaller values (ANSV) and the ...

In this paper, we propose efficient parallel algorithms on the EREW PRAM for optimally locating in a tree network a path-shaped facility and a tree-shaped facility of a specified length. Edges in the tree network have arbitrary positive lengths. Two ...

In this paper, we present a simple algorithm for solving the multipattern matching problem, with optimal speedup. The best-known deterministic parallel algorithm for this problem also provides optimal speedup, but relies crucially on a sophisticated ...

Sylow subgroups are fundamental in the design of asymptotically efficient group-theoretic algorithms, just as they have been in the study of the structure of finite groups. We present efficient parallel (NC) algorithms for finding and conjugating Sylow ...

We introduce an on-line protocol which routes any set ofNpackets along shortest paths with congestionCand dilationDthrough an arbitrary network inO(C+D+logN) steps, with high probability. This time bound is optimal up to the additive logN, and it has ...

We study the parallel complexity of selecting thekth smallest ofnelements on the CRCW PRAM. We show that this problem can be solved inO(log logn+ logk/log logn) time andO(n) operations for all 1 k n/2, which is superior to existing deterministic bounds ...

We give parallel algorithms that solve the single-source shortest paths problem on a weighted, undirected graph withnvertices andmedges inO(tlgn) time andO((n3/t2)lgnlg(n/t)+mlgn) work, or inO(tlgn) time andO((n3/t3+mn/t)lgn) work for anytin the range ...

We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known ...

We consider the problem of computing the minimum ofnvalues, and several well-known generalizations prefix minima, range minima, and all nearest smaller values (ANSV) for input elements drawn from the integer domain 1 s, wheres n. In this article we give ...

Public-key cryptographic systems often involve raising elements of some group (e.g.,GF(2n),Z/NZ, or elliptic curves) to large powers. An important question is how fast this exponentiation can be done, which often determines whether a given system is ...

We present the first NC algorithm for schedulingnunit length tasks onmidentical processors for the case where the precedence constraint is an interval order. Our algorithm runs on a priority concurrent read, concurrent write parallel random access ...

It was shown previously that sortingnitems intonlocations with a polynomial number of processors requires (logn/loglogn) time. We sidestep this lower bound with the idea of padded sorting, or sortingnitems inton+o(n) locations. Because many problems do ...

We present parallel NC algorithms for recognizing a reducible flow graph (rfg) and for finding dominators, minimum feedback vertex sets, and a depth first search tree in an rfg. On ann-node rfg, all of these algorithms run inpolylog(n) time usingM(n) ...

Many combinatorial problems can be efficiently solved for partialk-trees (graphs of treewidth bounded byk). The edge-coloring problem is one of the well-known combinatorial problems for which no efficient algorithms were previously known, except a ...

This paper considers the matrix chain product problem. This problem can be solved inO(nlogn) sequential time, while the best known parallel NC algorithm runs inO(log2n) time usingn6/log6nprocessors and inO(log3n) time withO(n2) time processor product. ...