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 $e$ has a color $c_e$ and a profit $p_e \in \mathbb{Q}^+$, we want to compute a maximum (cardinality or profit) matching in which no more than $w_j \in \mathbb{Z}^+$ edges of color $c_j$ 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 $w_j$ 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

Discrete Multi-modal Hashing with Canonical Views for Robust Mobile Landmark Search

Mobile landmark search (MLS) recently receives increasing attention for its great practical values. However, it still remains unsolved due to two important challenges. One is high bandwidth consumption of query transmission, and the other is the huge visual variations of query images sent from mobile devices. In this paper, we propose a novel hashing scheme, named as canonical view based discrete multi-modal hashing (CV-DMH), to handle these problems via a novel three-stage learning procedure. First, a submodular function is designed to measure visual representativeness and redundancy of a view set. With it, canonical views, which capture key visual appearances of landmark with limited redundancy, are efficiently discovered with an iterative mining strategy. Second, multi-modal sparse coding is applied to transform visual features from multiple modalities into an intermediate representation. It can robustly and adaptively characterize visual contents of varied landmark images with certain canonical views. Finally, compact binary codes are learned on intermediate representation within a tailored discrete binary embedding model which preserves visual relations of images measured with canonical views and removes the involved noises. In this part, we develop a new augmented Lagrangian multiplier (ALM) based optimization method to directly solve the discrete binary codes. We can not only explicitly deal with the discrete constraint, but also consider the bit-uncorrelated constraint and balance constraint together. Experiments on real world landmark datasets demonstrate the superior performance of CV-DMH over several state-of-the-art methods

Sizing-stiffened composite panels loaded in the postbuckling range

Stiffened panels are widely used in aircraft structures such as wing covers, fuselages, control surfaces, spar webs, bulkheads, and floors. The detailed sizing of minimum-weight stiffened panels involves many considerations. Use of composite materials introduces additional complexities. Many potential modes of failure exist. Analyses for these modes are often not trivial, especially for those involving large out-of-plane displacements. Accurate analyses of all potential failure modes are essential. Numerous practical constraints arise from manufacturing/cost considerations and from damage tolerance, durability, and stiffness requirements. The number of design variables can be large when lamina thicknesses and stacking sequence are being optimized. A significant burden is placed on the sizing code due to the complex analyses, practical constraints, and number of design variables. On the other hand, sizing weight-efficient panels without the aid of an automated procedure is almost out of the question. The sizing code postbuckled Open-Stiffener Optimum Panels (POSTOP) has been developed to aid in the design of minimum-weight panels subject to the considerations mentioned above. Developed for postbuckled composite panels, POSTOP may be used for buckling resistant panels and metallic panels as well. The COPES/CONMIN optimizer is used in POSTOP although other options such as those in the ADS system could be substituted with relative ease. The basic elements of POSTOP are shown. Some of these elements and usage of the program are described