Flow Heuristics 1 and 2.

Modules
		netmic.algorithmic_utility netmic.network_utility networkx time netmic.timer netmic.heuristics.weight_functions

Classes
		heuristicEll0StartSolution heuristicSolver heuristic1Solver heuristic1_1Solver heuristic1_2Solver heuristic1_3Solver(heuristic1Solver, heuristicx_3Solver) heuristic2Solver heuristic2_2Solver heuristic2_3Solver(heuristic2Solver, heuristicx_3Solver) heuristicx_3Solver   class heuristic1Solver(heuristicSolver)     base class for heuristic1, start with l1-opt INC, compute iteratively shortest paths between nodes with excess     Methods defined here: __init__(self, N) computeStartSolution(self) Return an initial solution for N, feasible regarding bounds, but not flow conservation, by computing the max-flow. solve(self)   class heuristic1_1Solver(heuristic1Solver)     Implementation of heuristic 1.1     Method resolution order: heuristic1_1Solver heuristic1Solver heuristicSolver Methods defined here: solve(self, sp='dijkstra', timelimit=900) Compute heuristic 1.1. Start flow is given by bound feasible max-flow, simple 0/1/2 weights for all nodes at once are used. The SP- computations are done using the method indicated by sp. Methods inherited from heuristic1Solver: __init__(self, N) computeStartSolution(self) Return an initial solution for N, feasible regarding bounds, but not flow conservation, by computing the max-flow.   class heuristic1_2Solver(heuristic1Solver)     Implementation of heuristic 1.2     Method resolution order: heuristic1_2Solver heuristic1Solver heuristicSolver Methods defined here: solve(self, timelimit=900) Compute heuristic 1.2. Start flow is given by bound feasible max-flow, 0/1-weights are computed "exact" for every pair (s,t) in (S,T). Methods inherited from heuristic1Solver: __init__(self, N) computeStartSolution(self) Return an initial solution for N, feasible regarding bounds, but not flow conservation, by computing the max-flow.   class heuristic1_3Solver(heuristic1Solver, heuristicx_3Solver)     Implementation of heuristic 1.3     Method resolution order: heuristic1_3Solver heuristic1Solver heuristicSolver heuristicx_3Solver Methods defined here: __init__(self, N, variant=False) solve(self, timelimit=900) Compute heuristic 1.3. Start flow is given by bound feasible max-flow, -1/0/1-weights are computed "exact" for every pair (s,t) in (S,T), then the shortest path is computed heuristically. Methods inherited from heuristic1Solver: computeStartSolution(self) Return an initial solution for N, feasible regarding bounds, but not flow conservation, by computing the max-flow. Methods inherited from heuristicx_3Solver: shortPathWithNegCycles(self, s, t=None) Return short path between s and t. This is essentially Dijkstra, adapted to tolerate negative weights and thereby no longer yielding the optimal solution.   class heuristic2Solver(heuristicSolver)     base class for heuristic2, start with heuristic ell_0 solution, compute iteratively shortest paths from node with largest excess     Methods defined here: __init__(self, N, timelimit=900) solve(self)   class heuristic2_2Solver(heuristic2Solver)     Implementation of heuristic 2.2     Method resolution order: heuristic2_2Solver heuristic2Solver heuristicSolver Methods defined here: solve(self) Compute heuristic 2.2. Start flow is given by bound-feasible, heuristic ell_0 INC, shortest path is computed with binary weights for node with largest excess. Methods inherited from heuristic2Solver: __init__(self, N, timelimit=900)   class heuristic2_3Solver(heuristic2Solver, heuristicx_3Solver)     Implementation of heuristic 2.3     Method resolution order: heuristic2_3Solver heuristic2Solver heuristicSolver heuristicx_3Solver Methods defined here: __init__(self, N, variant=False, timelimit=900) solve(self) Compute heuristic 2.3. Start flow is given by bound-feasible, heuristic ell_0 INC, shortest path is computed with ternary weights for node with largest excess, then shortest path is computed heuristically. Methods inherited from heuristicx_3Solver: shortPathWithNegCycles(self, s, t=None) Return short path between s and t. This is essentially Dijkstra, adapted to tolerate negative weights and thereby no longer yielding the optimal solution.   class heuristicEll0StartSolution     compute INC solution by iteratively satisfying node with smallest excess     Methods defined here: __init__(self, N) solve(self, timelimit=300) Return bound-feasible solution with (heuristically) as much nodes satisfied as possible.   class heuristicSolver     base class for heuristic, provide functionality shared by all heuristics     Methods defined here: __init__(self, N) solve(self)   class heuristicx_3Solver(heuristicSolver)     base class for heuristics 1.3 and 2.3, compute shortest path with forbidden pairs     Methods defined here: __init__(self, variant) shortPathWithNegCycles(self, s, t=None) Return short path between s and t. This is essentially Dijkstra, adapted to tolerate negative weights and thereby no longer yielding the optimal solution. solve(self)

Functions
		heapify(...) Transform list into a heap, in-place, in O(len(heap)) time. heappop(...) Pop the smallest item off the heap, maintaining the heap invariant. heappush(...) heappush(heap, item) -> None. Push item onto heap, maintaining the heap invariant. heuristic1_1(N, sp='dijkstra', timelimit=900) Return cover obtained by heuristic 1.1. heuristic1_2(N, timelimit=900) Return cover obtained by heuristic 1.2. heuristic1_3(N, variant=False, timelimit=900) Return cover obtained by heuristic 1.3. heuristic2_2(N, timelimit=900) Return cover obtained by heuristic 2.2. heuristic2_3(N, variant=False, timelimit=900) Return cover obtained by heuristic 2.3.