2 research outputs found
Constraint Generation Algorithm for the Minimum Connectivity Inference Problem
Given a hypergraph , the Minimum Connectivity Inference problem asks for a
graph on the same vertex set as with the minimum number of edges such that
the subgraph induced by every hyperedge of is connected. This problem has
received a lot of attention these recent years, both from a theoretical and
practical perspective, leading to several implemented approximation, greedy and
heuristic algorithms. Concerning exact algorithms, only Mixed Integer Linear
Programming (MILP) formulations have been experimented, all representing
connectivity constraints by the means of graph flows. In this work, we
investigate the efficiency of a constraint generation algorithm, where we
iteratively add cut constraints to a simple ILP until a feasible (and optimal)
solution is found. It turns out that our method is faster than the previous
best flow-based MILP algorithm on random generated instances, which suggests
that a constraint generation approach might be also useful for other
optimization problems dealing with connectivity constraints. At last, we
present the results of an enumeration algorithm for the problem.Comment: 16 pages, 4 tables, 1 figur
Connectivity Inference in Mass Spectrometry based Structure Determination
International audienceWe consider the following Minimum Connectivity Inference problem (MCI), which arises in structural biology: given vertex sets V i ⊆ V, i ∈ I, find a graph G = (V,E) minimizing the size of the edge set E, such that the sub-graph of G induced by each V i is connected. This problem arises in structural biology, when one aims at finding the pairwise contacts between the proteins of a protein assembly, given the lists of proteins involved in sub-complexes. We present four contributions. First, using a reduction of the set cover problem, we establish that the MCI problem is APX-hard. Second, we show how to solve the problem to optimality using a mixed integer linear programming formulation (MILP). Third, we develop a greedy algorithm based on union-find data structures (Greedy), yielding a 2(log2 |V| + log2 κ)-approximation, with κ the maximum number of subsets V i a vertex belongs to. Fourth, application-wise, we use the MILP and the greedy heuristic to solve the aforementioned connectivity inference problem in structural biology. We show that the solutions of MILP and Greedy are more parsimonious with respect to edges than those reported by the algorithm initially developed in biophysics, which are not qualified in terms of optimality. Since MILP outputs a set of optimal solutions, we introduce the notion of consensus solution. Using assemblies whose pairwise contacts are known exhaustively, we show an almost perfect agreement between the contacts predicted by our algorithms and the experimentally determined ones, especially for consensus solutions