International audienceDetermining the hydrogen-deuterium exchange speeds of single residues from data for peptic fragments obtained by FT-ICS MS is currently mainly done by manual interpretation. We provide an automated method based on combinatorial optimization. More precisely, we present an algorithm that enumerates all possible exchange speeds for single residues that explain the observed data of the peptic fragments

√ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated min-cost flow problem on a planar bidirected graph with bounded costs and face sizes in O(n 3/2 ) time.

We present a method for solving the shortest transshipment problem-also known as uncapacitated minimum cost flow-up to a multiplicative error of 1 + ε in undirected graphs with non-negative integer edge weights using a tailored gradient descent algorithm. Our gradient descent algorithm takes ε −3 polylog n iterations, and in each iteration it needs to solve an instance of the transshipment problem up to a multiplicative error of polylog n, where n is the number of nodes. In particular, this allows us to perform a single iteration by computing a solution on a sparse spanner of logarithmic stretch. Using a careful white-box analysis, we can further extend the method to finding approximate solutions for the single-source shortest paths (SSSP) problem. As a consequence, we improve prior work by obtaining the following results: 1. Broadcast CONGEST model:) rounds, 1 where D is the (hop) diameter of the network. 2. Broadcast congested clique model: (1+ε)-approximate shortest transshipment and SSSP using O(ε −O(1) ) rounds. Multipass streaming model:(1 + ε)-approximate shortest transshipment and SSSP usingÕ(n) space andÕ(ε −O(1) ) passes. The previously fastest SSSP algorithms for these models leverage sparse hop sets. We bypass the hop set construction; computing a spanner is sufficient with our method. The above bounds assume non-negative integer edge weights that are polynomially bounded in n; for general nonnegative weights, running times scale with the logarithm of the maximum ratio between non-zero weights. In case of asymmetric costs for traversing an edge in opposite directions, running times scale with the maximum ratio between the costs of both directions over all edges.

This article surveys combinatorial optimization as a flexible and powerful tool for computational generation and adaptation of graphical user interfaces (GUIs).

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