4,571 research outputs found
Selection from read-only memory with limited workspace
Given an unordered array of elements drawn from a totally ordered set and
an integer in the range from to , in the classic selection problem
the task is to find the -th smallest element in the array. We study the
complexity of this problem in the space-restricted random-access model: The
input array is stored on read-only memory, and the algorithm has access to a
limited amount of workspace. We prove that the linear-time prune-and-search
algorithm---presented in most textbooks on algorithms---can be modified to use
bits instead of words of extra space. Prior to our
work, the best known algorithm by Frederickson could perform the task with
bits of extra space in time. Our result separates
the space-restricted random-access model and the multi-pass streaming model,
since we can surpass the lower bound known for the latter
model. We also generalize our algorithm for the case when the size of the
workspace is bits, where . The running time
of our generalized algorithm is ,
slightly improving over the
bound of Frederickson's algorithm. To obtain the improvements mentioned above,
we developed a new data structure, called the wavelet stack, that we use for
repeated pruning. We expect the wavelet stack to be a useful tool in other
applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201
Fast Deterministic Selection
The Median of Medians (also known as BFPRT) algorithm, although a landmark
theoretical achievement, is seldom used in practice because it and its variants
are slower than simple approaches based on sampling. The main contribution of
this paper is a fast linear-time deterministic selection algorithm
QuickselectAdaptive based on a refined definition of MedianOfMedians. The
algorithm's performance brings deterministic selection---along with its
desirable properties of reproducible runs, predictable run times, and immunity
to pathological inputs---in the range of practicality. We demonstrate results
on independent and identically distributed random inputs and on
normally-distributed inputs. Measurements show that QuickselectAdaptive is
faster than state-of-the-art baselines.Comment: Pre-publication draf
Median computation in graphs using consensus strategies
Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review ofalgorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed.majority strategy;consensus strategy;Hill climbing median computation
Observer Placement for Source Localization: The Effect of Budgets and Transmission Variance
When an epidemic spreads in a network, a key question is where was its
source, i.e., the node that started the epidemic. If we know the time at which
various nodes were infected, we can attempt to use this information in order to
identify the source. However, maintaining observer nodes that can provide their
infection time may be costly, and we may have a budget on the number of
observer nodes we can maintain. Moreover, some nodes are more informative than
others due to their location in the network. Hence, a pertinent question
arises: Which nodes should we select as observers in order to maximize the
probability that we can accurately identify the source? Inspired by the simple
setting in which the node-to-node delays in the transmission of the epidemic
are deterministic, we develop a principled approach for addressing the problem
even when transmission delays are random. We show that the optimal
observer-placement differs depending on the variance of the transmission delays
and propose approaches in both low- and high-variance settings. We validate our
methods by comparing them against state-of-the-art observer-placements and show
that, in both settings, our approach identifies the source with higher
accuracy.Comment: Accepted for presentation at the 54th Annual Allerton Conference on
Communication, Control, and Computin
- …