We give anO(n log n)-time linear-space algorithm that, given a plane 3-tree G with n vertices and a set S of n points in the plane, determines whether G has a point-set embedding on S (i.e., a planar straight-line drawing of G where each vertex is mapped to a distinct point of S), improving the O(n)-time O(n)-space algorithm of Moosa and Rahman. Given an arbitrary plane graph G and a point set ...

In this work, we propose APLASIA, an holistic architecture with a radical design. Aiming at simplifying the inner network devices (and so their cost), we tradeoff node architectureand algorithmic-complexity for an increased (but tunable) communication cost. The main ingredients of our recipe are (i) the use of complete paths directly in the frames header, that allows core devices to perform dat...

We introduce a new way of generating cutting planes of a mixed integer programme by way of taking binary variables. Four binary variables are introduced to form quartic inequalities, which results in a reduced first-level mixed integer programme. A new way of weakening the inequalities is presented. An algorithm to carryout the separation of the inequalities, which are exponential in number, is...

In this paper, we present an optimal O(n) time algorithm for deciding if a metric space (X, d) on n points can be isometrically embedded into the plane endowed with the l1-metric. It improves the O(n 2 log n) time algorithm of J. Edmonds (2008). Together with some ingredients introduced by Edmonds, our algorithm uses the concept of tight span and the injectivity of the l1-plane. A different O(n...

In this paper, we present an optimal O(n) time algorithm for deciding if a metric space (X, d) on n points can be isometrically embedded into the plane endowed with the l1-metric. It improves the O(n 2 log n) time algorithm of J. Edmonds (2008). Together with some ingredients introduced by Edmonds, our algorithm uses the concept of tight span and the injectivity of the l1-plane. A different O(n...