160,303 research outputs found
Constant Factor Approximation for Capacitated k-Center with Outliers
The -center problem is a classic facility location problem, where given an
edge-weighted graph one is to find a subset of vertices ,
such that each vertex in is "close" to some vertex in . The
approximation status of this basic problem is well understood, as a simple
2-approximation algorithm is known to be tight. Consequently different
extensions were studied.
In the capacitated version of the problem each vertex is assigned a capacity,
which is a strict upper bound on the number of clients a facility can serve,
when located at this vertex. A constant factor approximation for the
capacitated -center was obtained last year by Cygan, Hajiaghayi and Khuller
[FOCS'12], which was recently improved to a 9-approximation by An, Bhaskara and
Svensson [arXiv'13].
In a different generalization of the problem some clients (denoted as
outliers) may be disregarded. Here we are additionally given an integer and
the goal is to serve exactly clients, which the algorithm is free to
choose. In 2001 Charikar et al. [SODA'01] presented a 3-approximation for the
-center problem with outliers.
In this paper we consider a common generalization of the two extensions
previously studied separately, i.e. we work with the capacitated -center
with outliers. We present the first constant factor approximation algorithm
with approximation ratio of 25 even for the case of non-uniform hard
capacities.Comment: 15 pages, 3 figures, accepted to STACS 201
Online Matching with Stochastic Rewards: Optimal Competitive Ratio via Path Based Formulation
The problem of online matching with stochastic rewards is a generalization of
the online bipartite matching problem where each edge has a probability of
success. When a match is made it succeeds with the probability of the
corresponding edge. Introducing this model, Mehta and Panigrahi (FOCS 2012)
focused on the special case of identical edge probabilities. Comparing against
a deterministic offline LP, they showed that the Ranking algorithm of Karp et
al. (STOC 1990) is 0.534 competitive and proposed a new online algorithm with
an improved guarantee of for vanishingly small probabilities. For the
case of vanishingly small but heterogeneous probabilities Mehta et al. (SODA
2015), gave a 0.534 competitive algorithm against the same LP benchmark. For
the more general vertex-weighted version of the problem, to the best of our
knowledge, no results being were previously known even for identical
probabilities.
We focus on the vertex-weighted version and give two improvements. First, we
show that a natural generalization of the Perturbed-Greedy algorithm of
Aggarwal et al. (SODA 2011), is competitive when probabilities
decompose as a product of two factors, one corresponding to each vertex of the
edge. This is the best achievable guarantee as it includes the case of
identical probabilities and in particular, the classical online bipartite
matching problem. Second, we give a deterministic competitive algorithm
for the previously well studied case of fully heterogeneous but vanishingly
small edge probabilities. A key contribution of our approach is the use of
novel path-based analysis. This allows us to compare against the natural
benchmarks of adaptive offline algorithms that know the sequence of arrivals
and the edge probabilities in advance, but not the outcomes of potential
matches.Comment: Preliminary version in EC 202
Parameterized Approximation Algorithms for Bidirected Steiner Network Problems
The Directed Steiner Network (DSN) problem takes as input a directed
edge-weighted graph and a set of
demand pairs. The aim is to compute the cheapest network for
which there is an path for each . It is known
that this problem is notoriously hard as there is no
-approximation algorithm under Gap-ETH, even when parametrizing
the runtime by [Dinur & Manurangsi, ITCS 2018]. In light of this, we
systematically study several special cases of DSN and determine their
parameterized approximability for the parameter .
For the bi-DSN problem, the aim is to compute a planar
optimum solution in a bidirected graph , i.e., for every edge
of the reverse edge exists and has the same weight. This problem
is a generalization of several well-studied special cases. Our main result is
that this problem admits a parameterized approximation scheme (PAS) for . We
also prove that our result is tight in the sense that (a) the runtime of our
PAS cannot be significantly improved, and (b) it is unlikely that a PAS exists
for any generalization of bi-DSN, unless FPT=W[1].
One important special case of DSN is the Strongly Connected Steiner Subgraph
(SCSS) problem, for which the solution network needs to strongly
connect a given set of terminals. It has been observed before that for SCSS
a parameterized -approximation exists when parameterized by [Chitnis et
al., IPEC 2013]. We give a tight inapproximability result by showing that for
no parameterized -approximation algorithm exists under
Gap-ETH. Additionally we show that when restricting the input of SCSS to
bidirected graphs, the problem remains NP-hard but becomes FPT for
Improved Algorithms for MST and Metric-TSP Interdiction
We consider the MST-interdiction problem: given a multigraph G = (V, E), edge weights {w_e >= 0}_{e in E}, interdiction costs {c_e >= 0}_{e in E}, and an interdiction budget B >= 0, the goal is to remove a subset R of edges of total interdiction cost at most B so as to maximize the w-weight of an MST of G-R:=(V,E-R).
Our main result is a 4-approximation algorithm for this problem. This improves upon the previous-best 14-approximation [Zenklusen, FOCS 2015]. Notably, our analysis is also significantly simpler and cleaner than the one in [Zenklusen, FOCS 2015]. Whereas Zenklusen uses a greedy algorithm with an involved analysis to extract a good interdiction set from an over-budget set, we utilize a generalization of knapsack called the tree knapsack problem that nicely captures the key combinatorial aspects of this "extraction problem." We prove a simple, yet strong, LP-relative approximation bound for tree knapsack, which leads to our improved guarantees for MST interdiction. Our algorithm and analysis are nearly tight, as we show that one cannot achieve an approximation ratio better than 3 relative to the upper bound used in our analysis (and the one in [Zenklusen, FOCS 2015]).
Our guarantee for MST-interdiction yields an 8-approximation for metric-TSP interdiction (improving over the 28-approximation in [Zenklusen, FOCS 2015]). We also show that maximum-spanning-tree interdiction is at least as hard to approximate as the minimization version of densest-k-subgraph
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A novel improved model for building energy consumption prediction based on model integration
Building energy consumption prediction plays an irreplaceable role in energy planning, management, and conservation. Constantly improving the performance of prediction models is the key to ensuring the efficient operation of energy systems. Moreover, accuracy is no longer the only factor in revealing model performance, it is more important to evaluate the model from multiple perspectives, considering the characteristics of engineering applications. Based on the idea of model integration, this paper proposes a novel improved integration model (stacking model) that can be used to forecast building energy consumption. The stacking model combines advantages of various base prediction algorithms and forms them into “meta-features” to ensure that the final model can observe datasets from different spatial and structural angles. Two cases are used to demonstrate practical engineering applications of the stacking model. A comparative analysis is performed to evaluate the prediction performance of the stacking model in contrast with existing well-known prediction models including Random Forest, Gradient Boosted Decision Tree, Extreme Gradient Boosting, Support Vector Machine, and K-Nearest Neighbor. The results indicate that the stacking method achieves better performance than other models, regarding accuracy (improvement of 9.5%–31.6% for Case A and 16.2%–49.4% for Case B), generalization (improvement of 6.7%–29.5% for Case A and 7.1%-34.6% for Case B), and robustness (improvement of 1.5%–34.1% for Case A and 1.8%–19.3% for Case B). The proposed model enriches the diversity of algorithm libraries of empirical models
Improved Heterogeneous Distance Functions
Instance-based learning techniques typically handle continuous and linear
input values well, but often do not handle nominal input attributes
appropriately. The Value Difference Metric (VDM) was designed to find
reasonable distance values between nominal attribute values, but it largely
ignores continuous attributes, requiring discretization to map continuous
values into nominal values. This paper proposes three new heterogeneous
distance functions, called the Heterogeneous Value Difference Metric (HVDM),
the Interpolated Value Difference Metric (IVDM), and the Windowed Value
Difference Metric (WVDM). These new distance functions are designed to handle
applications with nominal attributes, continuous attributes, or both. In
experiments on 48 applications the new distance metrics achieve higher
classification accuracy on average than three previous distance functions on
those datasets that have both nominal and continuous attributes.Comment: See http://www.jair.org/ for an online appendix and other files
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