The classical analysis of online algorithms, due to its worst-case nature, can be quite
pessimistic when the input instance at hand is far from worst-case. Often this is not an issue …

We study generalizations of the``Prophet Inequality''and``Secretary Problem'', where the
algorithm is restricted to an arbitrary downward-closed set system. For 0, 1 values, we give O …

We introduce a novel framework of Prophet Inequalities for combinatorial valuation
functions. For a (n on-monotone) submodular objective function over an arbitrary matroid …

We extend the standard online worst-case model to accommodate past experience which is
available to the online player in many practical scenarios. We do this by revealing a random …

This chapter introduces the random-order model in online algorithms. In this model, the input
is chosen by an adversary, then randomly permuted before being presented to the …

The study of online algorithms and competitive analysis provides a solid foundation for
studying the quality of irrevocable decision making when the data arrives in an online …

In the ordinal matroid secretary problem (MSP), candidates do not reveal numerical weights,
but the decision maker can still discern if a candidate is better than another. An algorithm α …

We define a generalization of the classical secretary problem called the matroid secretary
problem. In this problem, the elements of a matroid are presented to an online algorithm in …

In classical secretary problems, a sequence of $ n $ elements arrive in a uniformly random
order, and we want to choose a single item, or a set of size $ K $. The random order model …

Free order prophet inequalities bound the ratio between the expected value obtained by two
parties each selecting one value from a set of independent random variables: a “prophet” …