The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph G and a spanning tree T for it, and the goal is to augment T with a minimum set of edges Aug from G, such that T ∪Aug is 2-edge-connected. TAP has been widely studied in the sequential setting. The best known approximation ratio of 2 for the weighted case dates back to the work of Frederic...

Let $$\mathcal {H}=(V,\mathcal {E})$$ be a hypergraph with maximum edge size $$\ell $$ and degree $$\varDelta . For given positive integers $$b_v$$ , $$v\in V$$ set multicover in {H}$$ is of edges $$C \subseteq \mathcal {E}$$ such that every vertex v V belongs to at least C. Set the problem finding minimum-cardinality multicover. Peleg, Schechtman Wool conjectured for any fixed $$b:=\min _{v\in...

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239–269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLPFilter Algorithm, Technic...

A general approach to optimal motion synthesis of constrained multibody systems is presented. It applies to controlled mechanical systems such as industrial manipulators and legged-locomotion systems. An optimal control problem is stated. A parametric optimization technique based on approximating joint motion coordinates using spline functions of class C is developed to recast this primary prob...

Numerous government surveys of natural resources use Post-Stratifi cation to improve statistical effi ciency, where strata are defi ned by full-coverage, remotely sensed data and geopolitical boundaries. Recursive Restriction Estimation, which may be considered a special case of the static Kalman fi lter, is an attractive alternative. It decomposes a complex estimation problem into simple compo...

The amount of data produced by ubiquitous computing applications is quickly growing, due to the pervasive presence of small devices endowed with sensing, computing and communication capabilities. Heterogeneity and strong interdependence, which characterize ‘ubiquitous data’, require a (multi-)relational approach to their analysis. However, relational data mining algorithms do not scale well and...

The probability hypothesis density (PHD) filter is a first moment approximation to the evolution of a dynamic point process which can be used to approximate the optimal filtering equations of the multiple-object tracking problem. We show that, under reasonable assumptions, a sequential Monte Carlo (SMC) approximation of the PHD filter converges in mean of order p ≥ 1, and hence almost surely, t...

Energy efficiency (EE) is an important aspect of satellite communications. Different with the existing algorithms that typically use first-order Taylor lower bound approximation to convert non-convex EE maximization (EEM) problems into convex ones, in this letter a two-step quadratic transformation method presented. In first step, fractional form achievable rate over total power consumption con...

While very much impressed by the scope of the chimical reaction models handled by Professor Wilkinson, we will (presumably predictably!) focus on the simulation aspects of his paper. First, the solution proposed by the author to overcome the difficulties of handling the complex likelihood π(x|θ) reminds us of the auxiliary completion of Møller et al. (2006), who created (as well) an auxiliary d...