We present logspace algorithms for the canonical labeling problem and the representation problem of Helly circular-arc (HCA) graphs. The first step is a reduction to canonical labeling and representation of interval intersection matrices. In a second step, the Δ trees employed in McConnell’s linear time representation algorithm for interval matrices are adapted to the logspace setting and endow...

A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is Robinsonian precisely when the graph is a unit interval graph, so that Robinsonian matrices form a matrix analogue of the class of unit interval graphs. Here we prov...

Checking regularity (or singularity) of interval matrices is a known NP-hard problem. In this paper a general algorithm for checking regularity/singularity is presented which is not a priori exponential. The algorithm is based on a theoretical result according to which regularity may be judged from any single component of the solution set of an associated system of linear interval equations. Nu...

We study the structure of 01-matrices avoiding a pattern P as an interval minor. We focus on critical P -avoiders, i.e., on the P -avoiding matrices in which changing a 0-entry to a 1-entry always creates a copy of P as an interval minor. Let Q be the 3 × 3 permutation matrix corresponding to the permutation 231. As our main result, we show that for every pattern P that has no rotated copy of Q...

This note considers the stability of uncertain matrices. It is shown that under certain structural assumptions on the uncertain matrices the Schur stability can be assured from computing the numerical radius of the vertex matrices. This result is less conservative than that of using a simultaneous Lyapunov function method. Necessary and sufficient conditions are also obtained for the stability ...

We will denote intervals and interval vectors by Latin letters a, b, e . . . . (with or without index), interval matrices by capital Latin letters A, B, C , . . . Real vectors and matrices will be denoted by Latin letters with lower dots q, .b,e.,..., A., B., C . , . . . Endpoints of intervals and of interval vectors will be denoted by a_, ~ (lower and upper endpoims, respectively), real n u m ...

Stability analysis of linear circuits and systems under interval parameters uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the eigenvalues of interval matrices with complex eigenvalues, is considered. A method for computing such bounds is suggested. It consist of setting up and solving a sy...

A sufficient condition for the robust D-stability of dynamic interval systems is proposed in this paper. This D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of matrix inequalities defined at a series of partialvertex-based interval matrices other than the total vertex matrices as previous results. This condition is also extended ...