Based on the method of (n, k)-universal sets, we present a deterministic parameterized algorithm for the weighted rd-matching problem with time complexity O∗(4(r−1)k+o(k)), improving the previous best upper bound O∗(4rk+o(k)). In particular, the algorithm applied to the unweighted 3d-matching problem results in a deterministic algorithm with time O ∗(16k+o(k)), improving the previous best resul...

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as (3, 3)hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting problem for 3-partite (3, 3)-hypergraphs. The proof tech...

Motivated by a conjecture of Liang, we introduce a restricted path packing problem in bipartite graphs that we call a V-free 2-matching. We verify the conjecture through a weakening of the hypergraph matching problem. We close the paper by showing that it is NP-complete to decide whether one of the color classes of a bipartite graph can be covered by a V-free 2-matching.

We address in this paper automatic face verification from 3D (3-dimensional) facial surface and grey level analysis. 3D acquisition is performed by a structured light system, adapted to face capture and allowing grey level acquisition in alignment. The 3D facial shapes are compared and the residual error after 3D matching is used as a first similarity measure. A second similarity measure is der...

Low-cost RGB-D sensing technology, such as the Microsoft Kinect, is gaining acceptance in the scientific community and even entering into our homes. This technology enables ordinary users to capture everyday object into digital 3D representations. Considering the image retrieval context, whereas the ability to digitalize photos led to a rapid increase of large collections of images, which in tu...

IMPORTANCE Palpation of the nasal tip is an essential component of the preoperative rhinoplasty examination. Measuring tip support is challenging, and the forces that correspond to ideal tip support are unknown. OBJECTIVE To identify the integrated reaction force and the minimum and ideal mechanical properties associated with nasal tip support. DESIGN, SETTING, AND PARTICIPANTS Three-dimens...

In this note we consider the properties of the Hamming distance in combinatorial optimization problems on hypergraph matchings, also known as multidimensional assignment problems. It is shown that the Hamming distance between feasible solutions of hypergraph matching problems can be computed as an optimal value of linear assignment problem. For random hypergraph matching problems, an upper boun...

This study evaluated the feasibility of using three-dimensional printing (3DP) to fabricate porous titanium implants. Titanium powder was blended with a water-soluble binder material. Green, porous, titanium implants fabricated by 3DP were sintered under protective argon atmosphere at 1,200, 1,300, or 1,400°C. Sintered implant prototypes had uniform shrinkage and no obvious shape distortion aft...

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is [Formula: see text]-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-pa...