749 research outputs found
Solving 0-1 Knapsack Problem by Greedy Degree and Expectation Efficiency
It is well known that 0-1 knapsack problem (KP01) plays an important role in both computing theory and real life application. Due to its NP-hardness, lots of impressive research work has been performed on many variants of the problem. Inspired by region partition of items, an effective hybrid algorithm based on greedy degree and expectation efficiency (GDEE) is presented in this paper. In the proposed algorithm, initially determinate items region, candidate items region and unknown items region are generated to direct the selection of items. A greedy degree model inspired by greedy strategy is devised to select some items as initially determinate region. Dynamic expectation efficiency strategy is designed and used to select some other items as candidate region, and the remaining items are regarded as unknown region. To obtain the final items to which the best profit corresponds, static expectation efficiency strategy is proposed whilst the parallel computing method is adopted to update the objective function value. Extensive numerical investigations based on a large number of instances are conducted. The proposed GDEE algorithm is evaluated against chemical reaction optimization algorithm and modified discrete shuffled frog leaping algorithm. The comparative results show that GDEE is much more effective in solving KP01 than other algorithms and that it is a promising tool for solving combinatorial optimization problems such as resource allocation and production scheduling
Budget Feasible Mechanisms for Experimental Design
In the classical experimental design setting, an experimenter E has access to
a population of potential experiment subjects , each
associated with a vector of features . Conducting an experiment
with subject reveals an unknown value to E. E typically assumes
some hypothetical relationship between 's and 's, e.g., , and estimates from experiments, e.g., through linear
regression. As a proxy for various practical constraints, E may select only a
subset of subjects on which to conduct the experiment.
We initiate the study of budgeted mechanisms for experimental design. In this
setting, E has a budget . Each subject declares an associated cost to be part of the experiment, and must be paid at least her cost. In
particular, the Experimental Design Problem (EDP) is to find a set of
subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in
S}x_i\T{x_i}) under the constraint ; our objective
function corresponds to the information gain in parameter that is
learned through linear regression methods, and is related to the so-called
-optimality criterion. Further, the subjects are strategic and may lie about
their costs.
We present a deterministic, polynomial time, budget feasible mechanism
scheme, that is approximately truthful and yields a constant factor
approximation to EDP. In particular, for any small and , we can construct a (12.98, )-approximate mechanism that is
-truthful and runs in polynomial time in both and
. We also establish that no truthful,
budget-feasible algorithms is possible within a factor 2 approximation, and
show how to generalize our approach to a wide class of learning problems,
beyond linear regression
Improved Approximation Algorithms for Stochastic Matching
In this paper we consider the Stochastic Matching problem, which is motivated
by applications in kidney exchange and online dating. We are given an
undirected graph in which every edge is assigned a probability of existence and
a positive profit, and each node is assigned a positive integer called timeout.
We know whether an edge exists or not only after probing it. On this random
graph we are executing a process, which one-by-one probes the edges and
gradually constructs a matching. The process is constrained in two ways: once
an edge is taken it cannot be removed from the matching, and the timeout of
node upper-bounds the number of edges incident to that can be probed.
The goal is to maximize the expected profit of the constructed matching.
For this problem Bansal et al. (Algorithmica 2012) provided a
-approximation algorithm for bipartite graphs, and a -approximation for
general graphs. In this work we improve the approximation factors to
and , respectively.
We also consider an online version of the bipartite case, where one side of
the partition arrives node by node, and each time a node arrives we have to
decide which edges incident to we want to probe, and in which order. Here
we present a -approximation, improving on the -approximation of
Bansal et al.
The main technical ingredient in our result is a novel way of probing edges
according to a random but non-uniform permutation. Patching this method with an
algorithm that works best for large probability edges (plus some additional
ideas) leads to our improved approximation factors
Whom to Ask? Jury Selection for Decision Making Tasks on Micro-blog Services
It is universal to see people obtain knowledge on micro-blog services by
asking others decision making questions. In this paper, we study the Jury
Selection Problem(JSP) by utilizing crowdsourcing for decision making tasks on
micro-blog services. Specifically, the problem is to enroll a subset of crowd
under a limited budget, whose aggregated wisdom via Majority Voting scheme has
the lowest probability of drawing a wrong answer(Jury Error Rate-JER). Due to
various individual error-rates of the crowd, the calculation of JER is
non-trivial. Firstly, we explicitly state that JER is the probability when the
number of wrong jurors is larger than half of the size of a jury. To avoid the
exponentially increasing calculation of JER, we propose two efficient
algorithms and an effective bounding technique. Furthermore, we study the Jury
Selection Problem on two crowdsourcing models, one is for altruistic
users(AltrM) and the other is for incentive-requiring users(PayM) who require
extra payment when enrolled into a task. For the AltrM model, we prove the
monotonicity of JER on individual error rate and propose an efficient exact
algorithm for JSP. For the PayM model, we prove the NP-hardness of JSP on PayM
and propose an efficient greedy-based heuristic algorithm. Finally, we conduct
a series of experiments to investigate the traits of JSP, and validate the
efficiency and effectiveness of our proposed algorithms on both synthetic and
real micro-blog data.Comment: VLDB201
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