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Probabilistic analysis of algorithms for cost constrained minimum weighted combinatorial objects
arXiv - CS - Discrete Mathematics Pub Date : 2020-09-07 , DOI: arxiv-2009.03416
Alan Frieze and Tomasz Tkocz

We consider cost constrained versions of the minimum spanning tree problem and the assignment problem. We assume edge weights are independent copies of a continuous random variable $Z$ that satisfies $F(x)=\Pr(Z\leq x)\approx x^\alpha$ as $x\to0$, where $\alpha\geq 1$. Also, there are $r=O(1)$ budget constraints with edge costs chosen from the same distribution. We use Lagrangean duality to construct polynomial time algorithms that produce asymptotically optimal solutions. For the spanning tree problem, we allow $r>1$, but for the assignment problem we can only analyse the case $r=1$.

中文翻译:

成本约束最小加权组合对象算法的概率分析

我们考虑最小生成树问题和分配问题的成本约束版本。我们假设边权重是连续随机变量 $Z$ 的独立副本,它满足 $F(x)=\Pr(Z\leq x)\approx x^\alpha$ 作为 $x\to0$,其中 $\alpha\ geq 1 美元。此外,还有 $r=O(1)$ 的预算约束,边成本选自相同的分布。我们使用拉格朗日对偶来构造多项式时间算法,以产生渐近最优解。对于生成树问题,我们允许$r>1$,但对于赋值问题,我们只能分析$r=1$的情况。
更新日期:2020-09-09
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