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Some simple distributed algorithms for sparse networks
TLDR
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
Haplotyping Populations by Pure Parsimony: Complexity of Exact and Approximation Algorithms
TLDR
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
A mixed integer linear programming formulation of the optimal mean/Value-at-Risk portfolio problem
TLDR
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
The firefighter problem for graphs of maximum degree three
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.
Cycle bases in graphs characterization, algorithms, complexity, and applications
TLDR
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
Packing cycles in undirected graphs
TLDR
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 novel min-cost flow method for estimating transcript expression with RNA-Seq
TLDR
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 greedy approach to compute a minimum cycle basis of a directed graph
TLDR
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
Optimal skewed data allocation on multiple channels with flat broadcast per channel
TLDR
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
Classes of cycle bases
TLDR
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
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