It is shown that edge colourings with at most $2\Delta-1$ colours, and maximal matchings can be computed within deterministic rounds, where $\Delta$ is the maximum degree of the network.Expand

This paper proves that the problem is APX-hard and presents a 2k- 1-approximation algorithm for the case in which each genotype has at most k ambiguous positions, and gives a new integer-programming formulation that has (for the first time) a polynomial number variables and constraints.Expand

An extension of the Markovitz model, in which the variance has been replaced with the Value-at-Risk, is considered, and it is shown that the model leads to an NP-hard problem, but if the number of past observation T or theNumber of assets K are low, e.g. fixed to a constant, polynomial time algorithms exist.Expand

We show that the firefighter problem is NP-complete for trees of maximum degree three, but in P for graphs of maximum degree three if the fire breaks out at a vertex of degree at most two.

The state of knowledge on cycle bases is surveyed, different kinds of cycle bases are introduced, characterized in terms of their cycle matrix, and structural results and a priori length bounds are proved.Expand

The problem of finding a largest collection of edge-disjoint cycles in G, dubbed CYCLE PACKING, is addressed and it is shown that the problem is APX- hard but can be approximated within a factor of O(logn) by a simple greedy approach.Expand

A new very general method based on network flows for a multiassembly problem arising from isoform identification and quantification with RNA-Seq, which is general enough to encompass many of the previous proposals under the least sum of squares model.Expand

A very simple exact algorithm of complexity O(m4n), being as fast as the first algorithm proposed for this problem, and it is proved that these greedy approaches fail for more specialized subclasses of directed cycle bases.Expand

Several algorithms, based on dynamic programming, are presented which provide optimal solutions for N data items and K channels and a new heuristic is devised which is experimentally tested on some benchmarks whose popularities are characterized by Zipf distributions.Expand

An unitary classification accommodating these three classes of cycle bases and further including the following four relevant classes: 2-bases (or planar bases), weakly fundamental cycle bases, totally unimodular cycles, and integral cycle bases.Expand