A Memetic Algorithm for the Multidimensional Assignment Problem

The Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s have also a number of applications. In this paper we propose a memetic algorithm for MAP that is a combination of a genetic algorithm with a local search procedure. The main contribution of the paper is an idea of dynamically adjusted generation size, that yields an outstanding flexibility of the algorithm to perform well for both small and large fixed running times. The results of computational experiments for several instance families show that the proposed algorithm produces solutions of very high quality in a reasonable time and outperforms the state-of-the art 3-AP memetic algorithm.Comment: 14 page

Many-to-Many Graph Matching: a Continuous Relaxation Approach

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs which optimally aligns their structure. In the classical formulation of graph matching, only one-to-one correspondences between vertices are considered. However, in many applications, graphs cannot be matched perfectly and it is more interesting to consider many-to-many correspondences where clusters of vertices in one graph are matched to clusters of vertices in the other graph. In this paper, we formulate the many-to-many graph matching problem as a discrete optimization problem and propose an approximate algorithm based on a continuous relaxation of the combinatorial problem. We compare our method with other existing methods on several benchmark computer vision datasets.Comment: 1

Approximation Algorithms for the Max-Buying Problem with Limited Supply

We consider the Max-Buying Problem with Limited Supply, in which there are $n$ items, with $C_i$ copies of each item $i$, and $m$ bidders such that every bidder $b$ has valuation $v_{ib}$ for item $i$. The goal is to find a pricing $p$ and an allocation of items to bidders that maximizes the profit, where every item is allocated to at most $C_i$ bidders, every bidder receives at most one item and if a bidder $b$ receives item $i$ then $p_i \leq v_{ib}$. Briest and Krysta presented a 2-approximation for this problem and Aggarwal et al. presented a 4-approximation for the Price Ladder variant where the pricing must be non-increasing (that is, $p_1 \geq p_2 \geq \cdots \geq p_n$). We present an $e/(e-1)$-approximation for the Max-Buying Problem with Limited Supply and, for every $\varepsilon > 0$, a $(2+\varepsilon)$-approximation for the Price Ladder variant

A Local Computation Approximation Scheme to Maximum Matching

We present a polylogarithmic local computation matching algorithm which guarantees a (1-\eps)-approximation to the maximum matching in graphs of bounded degree.Comment: Appears in Approx 201

How Many Topics? Stability Analysis for Topic Models

Topic modeling refers to the task of discovering the underlying thematic structure in a text corpus, where the output is commonly presented as a report of the top terms appearing in each topic. Despite the diversity of topic modeling algorithms that have been proposed, a common challenge in successfully applying these techniques is the selection of an appropriate number of topics for a given corpus. Choosing too few topics will produce results that are overly broad, while choosing too many will result in the "over-clustering" of a corpus into many small, highly-similar topics. In this paper, we propose a term-centric stability analysis strategy to address this issue, the idea being that a model with an appropriate number of topics will be more robust to perturbations in the data. Using a topic modeling approach based on matrix factorization, evaluations performed on a range of corpora show that this strategy can successfully guide the model selection process.Comment: Improve readability of plots. Add minor clarification

Minimum Partial-Matching and Hausdorff RMS-Distance under Translation: Combinatorics and Algorithms

We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum in near-linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. In addition, we show how to compute a local minimum of the partial-matching RMS-distance under translation, in polynomial time

Explicit Computation of Input Weights in Extreme Learning Machines

We present a closed form expression for initializing the input weights in a multi-layer perceptron, which can be used as the first step in synthesis of an Extreme Learning Ma-chine. The expression is based on the standard function for a separating hyperplane as computed in multilayer perceptrons and linear Support Vector Machines; that is, as a linear combination of input data samples. In the absence of supervised training for the input weights, random linear combinations of training data samples are used to project the input data to a higher dimensional hidden layer. The hidden layer weights are solved in the standard ELM fashion by computing the pseudoinverse of the hidden layer outputs and multiplying by the desired output values. All weights for this method can be computed in a single pass, and the resulting networks are more accurate and more consistent on some standard problems than regular ELM networks of the same size.Comment: In submission for the ELM 2014 Conferenc

A Cryptographic Moving-Knife Cake-Cutting Protocol

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n-1 where n is the number of players, which is the minimum.Comment: In Proceedings IWIGP 2012, arXiv:1202.422