In this note we address the problems of obtaining guaranteed and as good as possible estimates of system parameters for linear discrete–time systems subject to bounded disturbances. Some existing results relevant for the set–membership parameter identification and outer–bounding are first reviewed. Then, a novel method for characterizing the consistent parameter set based on homothety is offere...

We provide simple, faster algorithms for the detection of cliques and dominating sets of fixed order. Our algorithms are based on reductions to rectangular matrix multiplication. We also describe an improved algorithm for diamonds detection.

The classical FEEDBACK VERTEX SET problem asks, for a given undirected graph G and an integer k, to find a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET has attracted a large amount of research in the parameterized setting, and subsequent kernelization and fixed-parameter algorithms have been a rich source of ideas in the field. In this paper we consider...

We show that the DOMINATING SET problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K1,3, the complete bipartite graph on four vertices where the two parts have one and three vertices, respectively) as an induced subgraph. We present an algorithm that uses 2 2)nO(1) time and polynomial space to decide whether a claw-free graph on n v...

We introduce an efficient level set framework to parameter estimation problems governed by parametrized partial differential equations. The main ingredients are: (i) an “admissible region” approach to parameter estimation; (ii) the certified reduced basis method for efficient and reliable solution of parametrized partial differential equations; and (iii) a parameter-space level set method for c...

A minimization (resp., maximization) problem is called fixed parameter (r, t)approximable for two functionsr, t if there exists an algorithm that given an integer k and a problem instance I with optimum value opt, finds either a feasible solution of value at most r(k) · k (resp., at least k/r(k)) or a certificate that k < opt (resp., k > opt), in time t(k) · |I|O(1). A problem is called fixed p...

Restriction mapping involves cleaving DNA clones at specific sites with enzymes to produce a set of fragments. These fragments have characteristic lengths which together constitute a multiset (a set allowing repeated elements) called the “fingerprint” of the clone. Clones that overlap with each other share common restriction fragments as long as the region of overlap contains at least two enzym...

Abstract In this paper we study the controllability for a Cauchy problem governed by nonlinear differential inclusion driven Sturm–Liouville type operator. particular, considered second order involves set-valued reaction term depending on parameter. The key tool in proof of result provide is multivalued version theorem recently proved Haddad–Yarou, here established an initial conditions monitor...

We consider the parameterized complexity of the Unique Coverage problem: given a family of sets and a parameter k, find a subfamily that covers at least k elements exactly once. This NP-complete problem has applications in wireless networks and radio broadcasting and is also a natural generalization of the well-known Max Cut problem. We show that this problem is fixed-parameter tractable with r...