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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)
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)
BACKGROUND There are many pathological conditions with hepatic iron overload. Classical definite diagnostic methods of these disorders are invasive and based on a direct tissue biopsy material. For the last years the role of MR imaging in liver diagnostics has been increasing. MRI shows changes of liver intensity in patients with hepatic iron overload.(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)
BACKGROUND Cavernous hemangiomas are the most frequent neoplasms of the liver and in routine clinical practice they often need to be differentiated from malignant tumors and other benign focal lesions. The purpose of this study is to evaluate whether diagnostic accuracy of magnetic resonance imaging (MRI) of hepatic hemangiomas, showing atypical pattern on(More)
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