Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of
them. 1 This informal yet practical definition captures the essence of the goal of direct …

A certifying algorithm is an algorithm that produces, with each output, a certificate or witness
(easy-to-verify proof) that the particular output has not been compromised by a bug. A user …

This tutorial summarizes recent advances in the convex relaxation of the optimal power flow
(OPF) problem, focusing on structural properties rather than algorithms. Part I presents two …

Parameterized complexity/multivariate complexity algorithmics is an exciting field of modern
algorithm design and analysis, with a broad range of theoretical and practical aspects that …

Algebraic graph theory is a cornerstone in the study of electrical networks ranging from
miniature integrated circuits to continental-scale power systems. Conversely, many …

Euclidean distance geometry is the study of Euclidean geometry based on the concept of
distance. This is useful in several applications where the input data consist of an incomplete …

SUMMARY A causal network is used in a number of areas as a depiction of patterns of
'influence'among sets of variables. In expert systems it is common to perform 'inference'by …

Historically, there is a close connection between geometry and optImization. This is
illustrated by methods like the gradient method and the simplex method, which are …

Modelling sequential data is important in many areas of science and engineering. Hidden
Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they …

When dealing with special graph classes and algorithmic problems on them, a main source
is the classical book of Golumbic, Algorithmic Graph Theory and Perfect Graphs [454]. The …