منابع مشابه
Fast Monotone Summation over Disjoint Sets
We study the problem of computing an ensemble of multiple sums where the summands in each sum are indexed by subsets of size p of an n-element ground set. More precisely, the task is to compute, for each subset of size q of the ground set, the sum over the values of all subsets of size p that are disjoint from the subset of size q. We present an arithmetic circuit that, without subtraction, sol...
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We construct sequences of finite sums [Formula: see text] and [Formula: see text] converging increasingly and decreasingly, respectively, to the Euler-Mascheroni constant γ at the geometric rate 1/2. Such sequences are easy to compute and satisfy complete monotonicity-type properties. As a consequence, we obtain an infinite product representation for [Formula: see text] converging in a monotone...
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In this work we present the first practical ( 1 e − ǫ ) -approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the decreasing-threshold procedure of Badanidiyuru and Vondrak (SODA 2014) with a smoother version of the measured continuous greedy algorithm of Feldman et al. (FOCS 2011). This enables us to...
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We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix M ∈ Rn×n can be decomposed as M = ΦU +Π0, where the rank of Φ is k < n, and Π0 denotes Euclidean projection onto the nullspace of Φ⊤. We call such LCPs projective. Our algorithm solves a monotone projective LCP to relati...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1949
ISSN: 0004-2080
DOI: 10.1007/bf02590465