A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree Prune-and-Regraft (SPR) distance between two phylogenetic trees. Our result improves on the very recent 2.5-approximation algorithm due to Shi, Feng, You and Wang (2015). Our algorithm is the first approximation algorithm for this problem that uses LP duality in its analysis

Layers and Matroids for the Traveling Salesman's Paths

Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive "generalized Gao-trees". We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the $s-t$ path TSP

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial tim

Split Scheduling with Uniform Setup Times

We study a scheduling problem in which jobs may be split into parts, where the parts of a split job may be processed simultaneously on more than one machine. Each part of a job requires a setup time, however, on the machine where the job part is processed. During setup a machine cannot process or set up any other job. We concentrate on the basic case in which setup times are job-, machine-, and sequence-independent. Problems of this kind were encountered when modelling practical problems in planning disaster relief operations. Our main algorithmic result is a polynomial-time algorithm for minimising total completion time on two parallel identical machines. We argue why the same problem with three machines is not an easy extension of the two-machine case, leaving the complexity of this case as a tantalising open problem. We give a constant-factor approximation algorithm for the general case with any number of machines and a polynomial-time approximation scheme for a fixed number of machines. For the version with objective minimising weighted total completion time we prove NP-hardness. Finally, we conclude with an overview of the state of the art for other split scheduling problems with job-, machine-, and sequence-independent setup times

Improved immunoradiometric assay for plasma renin

BACKGROUND: Our renin IRMA overestimated renin in plasmas with high prorenin-to-renin ratios. We suspected that the overestimation of renin was caused less by cross-reactivity of the renin-specific antibody with prorenin than by a conformational change of prorenin into an enzymatically active form during the assay. METHODS: Because the inactive form of prorenin converts slowly into an active form at low temperature, we raised the assay temperature from 22 degrees C to 37 degrees C, simultaneously shortening the incubation time from 24 to 6 h. The former IRMA was performed in <1 working day with these modifications. RESULTS: The comeasurement of prorenin as renin was eliminated. Reagents were stable at 37 degrees C, and the new and old IRMAs were comparable in terms of precision and accuracy. The functional lower limit of the assay (4 mU/L) was below the lower reference limit (9 mU/L). The modified IRMA agreed closely with the activities measured with an enzyme-kinetic assay. Results were not influenced by the plasma concentration of angiotensinogen. At normal angiotensinogen concentrations, the IRMA closely correlated with the classical enzyme-kinetic assay of plasma renin activity. CONCLUSION: The modified IRMA, performed at 37 degrees C, avoids interference by prorenin while retaining the desirable analytical characteristics of the older IRMA and requiring less time