2,622 research outputs found
Incremental Medians via Online Bidding
In the k-median problem we are given sets of facilities and customers, and
distances between them. For a given set F of facilities, the cost of serving a
customer u is the minimum distance between u and a facility in F. The goal is
to find a set F of k facilities that minimizes the sum, over all customers, of
their service costs.
Following Mettu and Plaxton, we study the incremental medians problem, where
k is not known in advance, and the algorithm produces a nested sequence of
facility sets where the kth set has size k. The algorithm is c-cost-competitive
if the cost of each set is at most c times the cost of the optimum set of size
k. We give improved incremental algorithms for the metric version: an
8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive
randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic
algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized
algorithm.
The algorithm is s-size-competitive if the cost of the kth set is at most the
minimum cost of any set of size k, and has size at most s k. The optimal
size-competitive ratios for this problem are 4 (deterministic) and e
(randomized). We present the first poly-time O(log m)-size-approximation
algorithm for the offline problem and first poly-time O(log m)-size-competitive
algorithm for the incremental problem.
Our proofs reduce incremental medians to the following online bidding
problem: faced with an unknown threshold T, an algorithm submits "bids" until
it submits a bid that is at least the threshold. It pays the sum of all its
bids. We prove that folklore algorithms for online bidding are optimally
competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via
Online Bidding
Stochastic Database Cracking: Towards Robust Adaptive Indexing in Main-Memory Column-Stores
Modern business applications and scientific databases call for inherently
dynamic data storage environments. Such environments are characterized by two
challenging features: (a) they have little idle system time to devote on
physical design; and (b) there is little, if any, a priori workload knowledge,
while the query and data workload keeps changing dynamically. In such
environments, traditional approaches to index building and maintenance cannot
apply. Database cracking has been proposed as a solution that allows on-the-fly
physical data reorganization, as a collateral effect of query processing.
Cracking aims to continuously and automatically adapt indexes to the workload
at hand, without human intervention. Indexes are built incrementally,
adaptively, and on demand. Nevertheless, as we show, existing adaptive indexing
methods fail to deliver workload-robustness; they perform much better with
random workloads than with others. This frailty derives from the inelasticity
with which these approaches interpret each query as a hint on how data should
be stored. Current cracking schemes blindly reorganize the data within each
query's range, even if that results into successive expensive operations with
minimal indexing benefit. In this paper, we introduce stochastic cracking, a
significantly more resilient approach to adaptive indexing. Stochastic cracking
also uses each query as a hint on how to reorganize data, but not blindly so;
it gains resilience and avoids performance bottlenecks by deliberately applying
certain arbitrary choices in its decision-making. Thereby, we bring adaptive
indexing forward to a mature formulation that confers the workload-robustness
previous approaches lacked. Our extensive experimental study verifies that
stochastic cracking maintains the desired properties of original database
cracking while at the same time it performs well with diverse realistic
workloads.Comment: VLDB201
General Bounds for Incremental Maximization
We propose a theoretical framework to capture incremental solutions to
cardinality constrained maximization problems. The defining characteristic of
our framework is that the cardinality/support of the solution is bounded by a
value that grows over time, and we allow the solution to be
extended one element at a time. We investigate the best-possible competitive
ratio of such an incremental solution, i.e., the worst ratio over all
between the incremental solution after steps and an optimum solution of
cardinality . We define a large class of problems that contains many
important cardinality constrained maximization problems like maximum matching,
knapsack, and packing/covering problems. We provide a general
-competitive incremental algorithm for this class of problems, and show
that no algorithm can have competitive ratio below in general.
In the second part of the paper, we focus on the inherently incremental
greedy algorithm that increases the objective value as much as possible in each
step. This algorithm is known to be -competitive for submodular objective
functions, but it has unbounded competitive ratio for the class of incremental
problems mentioned above. We define a relaxed submodularity condition for the
objective function, capturing problems like maximum (weighted) (-)matching
and a variant of the maximum flow problem. We show that the greedy algorithm
has competitive ratio (exactly) for the class of problems that satisfy
this relaxed submodularity condition.
Note that our upper bounds on the competitive ratios translate to
approximation ratios for the underlying cardinality constrained problems.Comment: fixed typo
Willingness to Pay: Referendum Contingent Valuation and Uncertain Project Benefits
This study uses contingent valuation (CV) methods to estimate the benefit of an environmental water quality project of the Tietê River and its tributaries that flow through the São Paulo, Brazil, Metropolitan Area (SPMA). This paper demonstrates the range alternative central tendency measures for WTP produced under alternative parametric and nonparametric approaches using data gathered from a recent referendum CV survey that was conducted in Brazil to analyze a large, multi-phase water quality improvement project. It explains why one of the most commonly used measures, the unrestricted mean of the conditional inverse distribution function of WTP, may be less desirable and more computationally intensive than simpler alternatives like the nonparametric mean of the marginal inverse distribution function.Water management, Economics, contingent valuation, econometric models, environmental impact analysis, economic development projects
Fully Dynamic Single-Source Reachability in Practice: An Experimental Study
Given a directed graph and a source vertex, the fully dynamic single-source
reachability problem is to maintain the set of vertices that are reachable from
the given vertex, subject to edge deletions and insertions. It is one of the
most fundamental problems on graphs and appears directly or indirectly in many
and varied applications. While there has been theoretical work on this problem,
showing both linear conditional lower bounds for the fully dynamic problem and
insertions-only and deletions-only upper bounds beating these conditional lower
bounds, there has been no experimental study that compares the performance of
fully dynamic reachability algorithms in practice. Previous experimental
studies in this area concentrated only on the more general all-pairs
reachability or transitive closure problem and did not use real-world dynamic
graphs.
In this paper, we bridge this gap by empirically studying an extensive set of
algorithms for the single-source reachability problem in the fully dynamic
setting. In particular, we design several fully dynamic variants of well-known
approaches to obtain and maintain reachability information with respect to a
distinguished source. Moreover, we extend the existing insertions-only or
deletions-only upper bounds into fully dynamic algorithms. Even though the
worst-case time per operation of all the fully dynamic algorithms we evaluate
is at least linear in the number of edges in the graph (as is to be expected
given the conditional lower bounds) we show in our extensive experimental
evaluation that their performance differs greatly, both on generated as well as
on real-world instances
The reverse greedy algorithm for the metric k-median problem
The Reverse Greedy algorithm (RGreedy) for the k-median problem works as
follows. It starts by placing facilities on all nodes. At each step, it removes
a facility to minimize the resulting total distance from the customers to the
remaining facilities. It stops when k facilities remain. We prove that, if the
distance function is metric, then the approximation ratio of RGreedy is between
?(log n/ log log n) and O(log n).Comment: to appear in IPL. preliminary version in COCOON '0
The Miracle of Compound Interest: Does our Intuition Fail?
When it comes to estimating the benefits of long-term savings, many people rely on their intuition. Focusing on the domain of retirement savings, we use a randomized experiment to explore people’s intuition about how money accumulates over time. We ask half of our sample to estimate future consumption given savings (the forward perspective). The other half of the sample is asked to estimate savings given future consumption (the backward perspective). From an economic point of view, both subsamples are asked identical questions. However, we discover a large “direction bias”: the perceived benefits of long-term savings are substantially higher when individuals adopt a backward perspective. Our findings have important impli- cations for economic modeling, in general, and for structuring advice and financial literacy programs, in particular.Behavioral economics;financial intuition;financial literacy;com- pound interest;retirement saving
Seismic Response of a Tall Building to Recorded and Simulated Ground Motions
Seismological modeling technologies are advancing to the stage of enabling fundamental simulation of earthquake fault ruptures, which offer new opportunities to simulate extreme ground motions for collapse safety assessment and earthquake scenarios for community resilience studies. With the goal toward establishing the reliability of simulated ground motions for performance-based engineering, this paper examines the response of a 20-story concrete moment frame building analyzed by nonlinear dynamic analysis under corresponding sets of recorded and simulated ground motions. The simulated ground motions were obtained through a larger validation study via the Southern California Earthquake Center (SCEC) Broadband Platform (BBP) that simulates magnitude 5.9 to 7.3 earthquakes. Spectral shape and significant duration are considered when selecting ground motions in the development of comparable sets of simulated and recorded ground motions. Structural response is examined at different intensity levels up to collapse, to investigate whether a statistically significant difference exists between the responses to simulated and recorded ground motions. Results indicate that responses to simulated and recorded ground motions are generally similar at intensity levels prior to observation of collapses. Collapse capacities are also in good agreement for this structure. However, when the structure was made more sensitive to effects of ground motion duration, the differences between observed collapse responses increased. Research is ongoing to illuminate reasons for the difference and whether there is a systematic bias in the results that can be traced back to the ground motion simulation techniques
Estimating Future Consumer Welfare Gains from Innovation: The Case of Digital Data Storage
We develop a quality-adjusted cost index to estimate expected returns to investments in new technologies. The index addresses the problem of measuring social benefits from innovations in service sector inputs, where real output is not directly observable. We forecast welfare gains from two U.S. Advanced Technology Program innovations equaling 25%-50% of expected price, and aggregate consumer benefits of 2 billion, relative to trends in existing technologies. Our model’s probabilistic parameters reflect uncertainty about prospective outcomes and in our hedonic estimates of shadow values for selected product attributes. The index can be readily adopted by research and development (R&D) managers in industry and government.
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