784 research outputs found
Weighted Fair Multicast Multigroup Beamforming under Per-antenna Power Constraints
A multi-antenna transmitter that conveys independent sets of common data to
distinct groups of users is considered. This model is known as physical layer
multicasting to multiple co-channel groups. In this context, the practical
constraint of a maximum permitted power level radiated by each antenna is
addressed. The per-antenna power constrained system is optimized in a maximum
fairness sense with respect to predetermined quality of service weights. In
other words, the worst scaled user is boosted by maximizing its weighted
signal-to-interference plus noise ratio. A detailed solution to tackle the
weighted max-min fair multigroup multicast problem under per-antenna power
constraints is therefore derived. The implications of the novel constraints are
investigated via prominent applications and paradigms. What is more, robust
per-antenna constrained multigroup multicast beamforming solutions are
proposed. Finally, an extensive performance evaluation quantifies the gains of
the proposed algorithm over existing solutions and exhibits its accuracy over
per-antenna power constrained systems.Comment: Under review in IEEE Transactions in Signal Processin
Robust Correlation Clustering
In this paper, we introduce and study the Robust-Correlation-Clustering problem: given a graph G = (V,E) where every edge is either labeled + or - (denoting similar or dissimilar pairs of vertices), and a parameter m, the goal is to delete a set D of m vertices, and partition the remaining vertices V D into clusters to minimize the cost of the clustering, which is the sum of the number of + edges with end-points in different clusters and the number of - edges with end-points in the same cluster. This generalizes the classical Correlation-Clustering problem which is the special case when m = 0. Correlation clustering is useful when we have (only) qualitative information about the similarity or dissimilarity of pairs of points, and Robust-Correlation-Clustering equips this model with the capability to handle noise in datasets.
In this work, we present a constant-factor bi-criteria algorithm for Robust-Correlation-Clustering on complete graphs (where our solution is O(1)-approximate w.r.t the cost while however discarding O(1) m points as outliers), and also complement this by showing that no finite approximation is possible if we do not violate the outlier budget. Our algorithm is very simple in that it first does a simple LP-based pre-processing to delete O(m) vertices, and subsequently runs a particular Correlation-Clustering algorithm ACNAlg [Ailon et al., 2005] on the residual instance. We then consider general graphs, and show (O(log n), O(log^2 n)) bi-criteria algorithms while also showing a hardness of alpha_MC on both the cost and the outlier violation, where alpha_MC is the lower bound for the Minimum-Multicut problem
Algorithms to Approximate Column-Sparse Packing Problems
Column-sparse packing problems arise in several contexts in both
deterministic and stochastic discrete optimization. We present two unifying
ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain
improved approximation algorithms for some well-known families of such
problems. As three main examples, we attain the integrality gap, up to
lower-order terms, for known LP relaxations for k-column sparse packing integer
programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set
packing (Bansal et al., Algorithmica, 2012), and go "half the remaining
distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and
Seymour on hypergraph matching (Combinatorica, 1993).Comment: Extended abstract appeared in SODA 2018. Full version in ACM
Transactions of Algorithm
Bi-Criteria and Approximation Algorithms for Restricted Matchings
In this work we study approximation algorithms for the \textit{Bounded Color
Matching} problem (a.k.a. Restricted Matching problem) which is defined as
follows: given a graph in which each edge has a color and a profit
, we want to compute a maximum (cardinality or profit)
matching in which no more than edges of color are
present. This kind of problems, beside the theoretical interest on its own
right, emerges in multi-fiber optical networking systems, where we interpret
each unique wavelength that can travel through the fiber as a color class and
we would like to establish communication between pairs of systems. We study
approximation and bi-criteria algorithms for this problem which are based on
linear programming techniques and, in particular, on polyhedral
characterizations of the natural linear formulation of the problem. In our
setting, we allow violations of the bounds and we model our problem as a
bi-criteria problem: we have two objectives to optimize namely (a) to maximize
the profit (maximum matching) while (b) minimizing the violation of the color
bounds. We prove how we can "beat" the integrality gap of the natural linear
programming formulation of the problem by allowing only a slight violation of
the color bounds. In particular, our main result is \textit{constant}
approximation bounds for both criteria of the corresponding bi-criteria
optimization problem
Solving optimal stopping problems via randomization and empirical dual optimization
In this paper we consider optimal stopping problems in their dual form. In this way we reformulate the optimal stopping problem as a problem of stochastic average approximation (SAA) which can be solved via linear programming. By randomizing the initial value of the underlying process, we enforce solutions with zero variance while preserving the linear programming structure of the problem. A careful analysis of the randomized SAA algorithm shows that it enjoys favorable properties such as faster convergence rates and reduced complexity as compared to the non randomized procedure. We illustrate the performance of our algorithm on several benchmark examples
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