Lower Bounds for Bruss’ Odds Problem with Multiple Stoppings

Lower Bounds for Bruss' Odds Problem with Multiple Stoppings

This paper deals with Bruss’ odds problem with multiple stopping chances. A decision maker observes sequentially a sequence of independent 0/1 (failure/success) random variables with the objective to predict the last success correctly with multiple stopping chances. First, we give a nontrivial lower bound of the probability of win (obtaining the last success) for the problem with m-stoppings. N...

Some Lower Bounds for Estrada Index

Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given n-vertex graph G can be mapped to the vertices of a given h-vertex graph H such that each edge of G is mapped to an edge of H. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the 2-CSP problem. In this paper, we prove several lower bounds for HOM under the Exponen...

New Lower Bounds for Hopcroft's Problem

We establish new lower bounds on the complexity of the following basic geometric problem, attributed to John Hopcroft: Given a set of n points and m hyperplanes in IR, is any point contained in any hyperplane? We de ne a general class of partitioning algorithms, and show that in the worst case, for all m and n, any such algorithm requires time (n logm + nm + m logn) in two dimensions, or (n log...

Tight lower bounds for online labeling problem

We consider the file maintenance problem (also called the online labeling problem) in which n integer items from the set {1, . . . , r} are to be stored in an array of size m ≥ n. The items are presented sequentially in an arbitrary order, and must be stored in the array in sorted order (but not necessarily in consecutive locations in the array). Each new item must be stored in the array before...