24 research outputs found
Thresholds for Extreme Orientability
Multiple-choice load balancing has been a topic of intense study since the
seminal paper of Azar, Broder, Karlin, and Upfal. Questions in this area can be
phrased in terms of orientations of a graph, or more generally a k-uniform
random hypergraph. A (d,b)-orientation is an assignment of each edge to d of
its vertices, such that no vertex has more than b edges assigned to it.
Conditions for the existence of such orientations have been completely
documented except for the "extreme" case of (k-1,1)-orientations. We consider
this remaining case, and establish:
- The density threshold below which an orientation exists with high
probability, and above which it does not exist with high probability.
- An algorithm for finding an orientation that runs in linear time with high
probability, with explicit polynomial bounds on the failure probability.
Previously, the only known algorithms for constructing (k-1,1)-orientations
worked for k<=3, and were only shown to have expected linear running time.Comment: Corrected description of relationship to the work of LeLarg
Parallel Integer Polynomial Multiplication
We propose a new algorithm for multiplying dense polynomials with integer
coefficients in a parallel fashion, targeting multi-core processor
architectures. Complexity estimates and experimental comparisons demonstrate
the advantages of this new approach
An optimal parallel connectivity algorithm
AbstractA synchronized parallel algorithm of depth O(n2/p) for p (≤n2/log2 n) processors is given for the problem of computing connected components of an undirected graph. The speed-up of this algorithm is optimal in the sense that the depth of the algorithm is of the order of the running time of the fastest known sequential algorithm over the number of processors used
A taxonomy of problems with fast parallel algorithms
The class NC consists of problems solvable very fast (in time polynomial in log n) in parallel with a feasible (polynomial) number of processors. Many natural problems in NC are known; in this paper an attempt is made to identify important subclasses of NC and give interesting examples in each subclass. The notion of NC1-reducibility is introduced and used throughout (problem R is NC1-reducible to problem S if R can be solved with uniform log-depth circuits using oracles for S). Problems complete with respect to this reducibility are given for many of the subclasses of NC. A general technique, the “parallel greedy algorithm,” is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in NC2 (solvable by uniform Boolean circuits of depth O(log2 n) and polynomial size). The class LOGCFL is given a new characterization in terms of circuit families. The class DET of problems reducible to integer determinants is defined and many examples given. A new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph. This paper is a revised version of S. A. Cook, (1983, in “Proceedings 1983 Intl. Found. Comut. Sci. Conf.,” Lecture Notes in Computer Science Vol. 158, pp. 78–93, Springer-Verlag, Berlin/New York)
A New Data Layout For Set Intersection on GPUs
Set intersection is the core in a variety of problems, e.g. frequent itemset
mining and sparse boolean matrix multiplication. It is well-known that large
speed gains can, for some computational problems, be obtained by using a
graphics processing unit (GPU) as a massively parallel computing device.
However, GPUs require highly regular control flow and memory access patterns,
and for this reason previous GPU methods for intersecting sets have used a
simple bitmap representation. This representation requires excessive space on
sparse data sets. In this paper we present a novel data layout, "BatMap", that
is particularly well suited for parallel processing, and is compact even for
sparse data.
Frequent itemset mining is one of the most important applications of set
intersection. As a case-study on the potential of BatMaps we focus on frequent
pair mining, which is a core special case of frequent itemset mining. The main
finding is that our method is able to achieve speedups over both Apriori and
FP-growth when the number of distinct items is large, and the density of the
problem instance is above 1%. Previous implementations of frequent itemset
mining on GPU have not been able to show speedups over the best single-threaded
implementations.Comment: A version of this paper appears in Proceedings of IPDPS 201
Structure of computations in parallel complexity classes
Issued as Annual report, and Final project report, Project no. G-36-67
Fast Parallel Algorithms for the Subgraph Homeomorphism & the Subgraph Isomorphism Problems for Classes of Planar Graphs
23 pagesWe consider the problems of subgraph homeomorphism with fixed pattern graph,
recognition, and subgraph isomorphism for some classes of planar graphs. Following
the results of Robertson and Seymour on forbidden minor characterization, we show
that the problems of fixed subgraph homeomorphism and recognition for any family
of planar graphs closed under minor taking are in NC (i.e., they can be solved by an
algorithm running in poly-log time using polynomial number of processors). We also
show that the related subgraph isomorphism problem for biconnected outerplanar
·graphs is in NC. This is the first example of a restriction of subgraph isomorphism
to a non-trivial graph family admitting an NC algorith