The phrase "augmenting path" is correct and usable in written English.
It is typically used in the context of graph theory and algorithms, particularly in discussions about network flow and matching problems.
Example: "To find the maximum flow in the network, we need to identify an augmenting path."
Alternatives: "increasing path" or "enhancing path".
We exploit the shortest augmenting path algorithm for finding maximum value transversal (MVT) as well as block triangular forms (BTFs).
The main contribution of this paper is an efficient parallelization of the augmenting path search phase of the Hungarian algorithm.
It is concluded that for dense bipartite graphs, the auction algorithm scales well, and for sparse bipartite graphs at least a substantial speedup is achieved against alternative approaches that are based on augmenting path algorithms.
If the "starving" destination set D ≠ ϕ and augmenting path exists, then go back to Step 4 to find the possible augmenting path for the existing "starving" nodes.
The improved Dinic algorithm employs the DFS to solve the augmenting path.
By applying the augmenting path algorithm, the fiow for D j has been changed to f i ′, where f i ′ = f i + τ ( P j ).
We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a test set comprised of a wide range of real-world instances.
The algorithm was implemented in Python 2.6 using the NetworkX (Hagberg et al., 2008) package, as well as Joris van Rantwijk's implementation of the maximum-weight mapping algorithm based on the blossom method for finding augmenting paths and the primal dual method for finding a maximum-weight matching (Galil, 1986).
In fact, by starting from a null flow in N′, at each iteration of the procedure an augmenting flow saturates a path in N′ from a certain lowest aii′ to a certain highest bjj′, with i′ < j′ (because of the first step): the value of such an augmenting flow can be charged onto qii′jj′, which may be updated at each iteration.
We propose two algorithms, the random augmenting approach (RPA) and the Hamilton-path based approach (HPA), for finding the approximately longest simple path in a network.
Technological progress The model specifies labor augmenting technological progress, which we calibrate to the path provided by AWG.
