Finding a dominating set on bipartite graphs

Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O^∗(²n−z), where n is the number of vertices of G. As a consequence, our algorithm is able to solve the dominating set problem on bipartite graphs in time O^∗(²n/2). Another implication is an algorithm for general graphs whose running time is O(n^1.7088).     

Capturing crossings: Convex hulls of segment and plane intersections

We give a simple O(nlogn) algorithm to compute the convex hull of the (possibly Θ(n²)) intersection points in an arrangement of n line segments in the plane. We also show an arrangement of dn hyperplanes in d-dimensions whose arrangement has Θ(nd−1) intersection points on the convex hull.     

Sorting streamed multisets

Sorting is a classic problem and one to which many others reduce easily. In the streaming model, however, we are allowed only one pass over the input and sublinear memory, so in general we cannot sort. In this paper we show that, to determine the sorted order of a multiset s of size n containing σ?2 distinct elements using one pass and o(nlogσ) bits of memory, it is generally necessary and sufficient that its entropy H=o(logσ). Specifically, if s={s₁,…,sn} and si₁,…,sin is the stable sort of s, then we can compute i₁,…,in in one pass using O((H+1)n) time and O(Hn) bits of memory, with a simple combination of classic techniques. On the other hand, in the worst case it takes that much memory to compute any sorted ordering of s in one pass.     

A tree-covering problem arising in integrity of tree-structured data

We introduce and solve a problem motivated by integrity verification in third-party data distribution: Given an undirected tree, find a minimum-cardinality set of simple paths that cover all the tree edges and, secondarily, have smallest total path lengths. We give a linear time algorithm for this problem.     

On the tractability of coloring semirandom graphs

As part of the efforts to understand the intricacies of the k-colorability problem, different distributions over k-colorable graphs have been analyzed. While the problem is notoriously hard (not even reasonably approximable) in the worst case, the average case (with respect to such distributions) often turns out to be “easy”. Semi-random models mediate between these two extremes and are more suitable to imitate “real-life” instances than purely random models. In this work we consider semi-random variants of the planted k-colorability distribution. This continues a line of research pursued by Coja-Oghlan, and by Krivelevich and Vilenchik. Our aim is to study a more general semi-random framework than those suggested so far. On the one hand we show that previous algorithmic techniques extend to our more general semi-random setting; on the other hand we give a hardness result, proving that a closely related semi-random model is intractable. Thus we provide some indication about which properties of the input distribution make the k-colorability problem hard.     

Approximation algorithm for coloring of dotted interval graphs

Dotted interval graphs were introduced by Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348] as a generalization of interval graphs. The problem of coloring these graphs found application in high-throughput genotyping. Jiang [M. Jiang, Approximating minimum coloring and maximum independent set in dotted interval graphs, Information Processing Letters 98 (2006) 29-33] improves the approximation ratio of Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348]. In this work we improve the approximation ratio of Jiang [M. Jiang, Approximating minimum coloring and maximum independent set in dotted interval graphs, Information Processing Letters 98 (2006) 29-33] and Aumann et al. [Y. Aumann, M. Lewenstein, O. Melamud, R. Pinter, Z. Yakhini, Dotted interval graphs and high throughput genotyping, in: ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, pp. 339-348]. In the exposition we develop a generalization of the problem of finding the maximum number of non-attacking queens on a triangle.     

Supervised classification of share price trends

Share price trends can be recognized by using data clustering methods. However, the accuracy of these methods may be rather low. This paper presents a novel supervised classification scheme for the recognition and prediction of share price trends. We first produce a smooth time series using zero-phase filtering and singular spectrum analysis from the original share price data. We train pattern classifiers using the classification results of both original and filtered time series and then use these classifiers to predict the future share price trends. Experiment results obtained from both synthetic data and real share prices show that the proposed method is effective and outperforms the well-known K-means clustering algorithm.     

Reconstructing head models from photographs for individualized 3D‐audio processing

Visual fidelity and interactivity are the main goals in Computer Graphics research, but recently also audio is assuming an important role. Binaural rendering can provide extremely pleasing and realistic three‐dimensional sound, but to achieve best results it's necessary either to measure or to estimate individual Head Related Transfer Function (HRTF). This function is strictly related to the peculiar features of ears and face of the listener. Recent sound scattering simulation techniques can calculate HRTF starting from an accurate 3D model of a human head. Hence, the use of binaural rendering on large scale (i.e. video games, entertainment) could depend on the possibility to produce a sufficiently accurate 3D model of a human head, starting from the smallest possible input. In this paper we present a completely automatic system, which produces a 3D model of a head starting from simple input data (five photos and some key‐points indicated by user). The geometry is generated by extracting information from images and accordingly deforming a 3D dummy to reproduce user head features. The system proves to be fast, automatic, robust and reliable: geometric validation and preliminary assessments show that it can be accurate enough for HRTF calculation.     

Practical Product Importance Sampling for Direct Illumination

We present a practical algorithm for sampling the product of environment map lighting and surface reflectance. Our method builds on wavelet‐based importance sampling, but has a number of important advantages over previous methods. Most importantly, we avoid using precomputed reflectance functions by sampling the BRDF on‐the‐fly. Hence, all types of materials can be handled, including anisotropic and spatially varying BRDFs, as well as procedural shaders. This also opens up for using very high resolution, uncompressed, environment maps. Our results show that this gives a significant reduction of variance compared to using lower resolution approximations. In addition, we study the wavelet product, and present a faster algorithm geared for sampling purposes. For our application, the computations are reduced to a simple quadtree‐based multiplication. We build the BRDF approximation and evaluate the product in a single tree traversal, which makes the algorithm both faster and more flexible than previous methods.     

Real-Time GPU Silhouette Refinement using Adaptively Blended Bézier Patches

We present an algorithm for detecting and extracting the silhouette edges of a triangle mesh in real time using Graphical Processing Units (GPUs). We also propose a tessellation strategy for visualizing the mesh with smooth silhouettes through a continuous blend between Bézier patches with varying level of detail. Furthermore, we show how our techniques can be integrated with displacement and normal mapping. We give details on our GPU implementation and provide a performance analysis with respect to mesh size.