Bounds on the size of branch-and-bound proofs for integer knapsacks
نویسنده
چکیده
Using a direct counting argument, we derive lower and upper bounds for the number of nodes enumerated by linear programming-based branch-and-bound (B&B) method to prove the infeasibility of an integer knapsack problem. We prove by example that the size of the B&B tree could be exponential in the worst case.
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ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...
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ورودعنوان ژورنال:
- Oper. Res. Lett.
دوره 36 شماره
صفحات -
تاریخ انتشار 2008