寻找最大连续子和问题与（min，+）-卷积的超线性下界
Searching for a superlinear lower bounds for the Maximum Consecutive Subsums Problem and the (min,+)-convolution
摘要：
给定一个n个数的序列，最大连续子和问题（MCSP）要求对每个l = 1，...，n.没有算法是已知的这个问题，这是显着优于天真的二次解决方案。也没有一个超线性下限是已知的。MCSP最著名的界是基于（min，+）-卷积的计算，这是另一个既不知道O（n^{2-ε}）上限也不知道超线性下限的问题。我们表明，这两个问题实际上是计算等价的，通过提供它们之间的线性减少。然后，我们集中在寻找超线性下界的问题，并提供经验证据的Ω（nlogn）下界的决策树模型中的两个问题。
英文摘要：
Given a sequence of n numbers, the Maximum Consecutive Subsums Problem (MCSP) asks for the maximum consecutive sum of lengths l for each l = 1,...,n. No algorithm is known for this problem which is significantly better than the naive quadratic solution. Nor a super linear lower bound is known. The best known bound for the MCSP is based on the the computation of the (min,+)-convolution, another problem for which neither an O(n^{2-ε}) upper bound is known nor a super linear lower bound. We show that the two problems are in fact computationally equivalent by providing linear reductions between them. Then, we concentrate on the problem of finding super linear lower bounds and provide empirical evidence for an Ω(nlogn) lower bounds for both problems in the decision tree model.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
