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Let G(n, c/n) and G r (n) be an n-node sparse random graph and a sparse random r-regular graph, respectively, and let I(n, r) and I(n, c) be the sizes of the largest independent set in G(n, c/n) and G r (n). The asymptotic value of I(n, c)/n as n → ∞, can be computed using the Karp-Sipser algorithm when c ≤ e. For random cubic graphs, r = 3, it is only(More)
We study several classes of related scheduling problems including the carpool problem, its generalization to arbitrary inputs and the chairman assignment problem. We derive both lower and upper bounds for online algorithms solving these problems. We show that the greedy algorithm is optimal among online algorithms for the chairman assignment problem and the(More)
In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and structured disjunctive cuts, especially the-branch split cuts introduced by Li and Richard (2008). By analyzing-dimensional lattice-free sets, we prove that every facet-defining inequality of the convex hull of(More)
A greedy algorithm for scheduling and digital printing with inputs in a convex polytope, and vertices of this polytope as successive outputs, has recently been proven to be bounded for any convex polytope in any dimension. This boundedness property follows readily from the existence of some invariant region for a dynamical system equivalent to the(More)
In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (2008). By analyzing-dimensional lattice-free sets, we prove that for every integer there exists a positive integer such that every facet-defining(More)
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