Evangelos Kranakis

TL;DR: In this paper, the authors introduce three broad categories of combinatorial games: constructing, transforming, and marking triangulations, and develop polynomial-time algorithms to determine who wins a given game under optimal play, and to find a winning strategy.

TL;DR: In this article , the authors consider a special case of the problem where the agents are probabilistic, i.e., every attempt to change direction is an independent Bernoulli trial with known probability, where p is the probability that a turn fails.

TL;DR: In this article, the authors considered the problem of finding the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored, regardless of the choice of the subset of unreliable robots by the adversary.

Abstract: We consider \textsc{Persistence}, a new online problem concerning optimizing weighted observations in a stream of data when the observer has limited buffer capacity. A stream of weighted items arrive one at a time at the entrance of a buffer with two holding locations. A processor (or observer) can process (observe) an item at the buffer location it chooses, deriving this way the weight of the observed item as profit. The main constraint is that the processor can only move {\em synchronously} with the item stream; as a result, moving from the end of the buffer to the entrance, it crosses paths with the item already there, and will never have the chance to process or even identify it. \textsc{Persistence}\ is the online problem of scheduling the processor movements through the buffer so that its total derived value is maximized under this constraint. We study the performance of the straight-forward heuristic {\em Threshold}, i.e., forcing the processor to "follow" an item through the whole buffer only if its value is above a threshold. We analyze both the optimal offline and Threshold algorithms in case the input stream is a random permutation, or its items are iid valued. We show that in both cases the competitive ratio achieved by the Threshold algorithm is at least $2/3$ when the only statistical knowledge of the items is the median of all possible values. We generalize our results by showing that Threshold, equipped with some minimal statistical advice about the input, achieves competitive ratios in the whole spectrum between $2/3$ and $1$, following the variation of a newly defined density-like measure of the input. This result is a significant improvement over the case of arbitrary input streams, since in this case we show that no online algorithm can achieve a competitive ratio better than $1/2$.

TL;DR: In this paper, the authors show that the variables X1,X2,X r are functionally dependent for the initialization init if and only if the quantity eval X 1,X 2, X r (ρ, init) is independent of ρ.