KnowraLinear programming relaxationLinked fromLinked fromThe 7 pages that link to Linear programming relaxation, each with the reason it gives.All 7Broader topic 1Related 5Compared with 1Linear programmingBroader topic: Relaxations provide bounds for harder problems with discrete decisions.Integer programmingRelated: It gives bounds and a tractable starting point for many integer-programming algorithms.Combinatorial optimizationRelated: Its bounds help branch-and-bound discard discrete regions that cannot improve the incumbent.Approximation algorithmRelated: Its fractional optimum can bound the discrete optimum and guide rounding into feasible solutions.Kőnig's theoremCompared with: Outside bipartite graphs, the natural matching and cover relaxations can have a gap.Blossom algorithmRelated: Without odd-set constraints, the matching relaxation can admit fractional solutions in nonbipartite graphs.Tutte's theorem on perfect matchingsRelated: Matching formulations require odd-set constraints to capture the obstructions reflected by Tutte's condition.