English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The problem of evacuating two robots from the disk in the face-to-face modelwas first introduced in [Czyzowicz et al., DISC'14], and extensively studied(along with many variations) ever since with respect to worst case analysis. Weinitiate the study of the same problem with respect to average case analysis,which is also equivalent to designing randomized algorithms for the problem.First we observe that algorithm $B_{2}$ of~[Czyzowicz et al., DISC'14] withworst case cost $WRS(B_{2}):=5.73906$ has average case cost$AVG(B_{2}):=5.1172$. Then we verify that none of the algorithms that inducedworst case cost improvements in subsequent publications has better average casecost, hence concluding that our problem requires the invention of newalgorithms. Then, we observe that a remarkable simple algorithm, $B_{1}$, hasvery small average case cost $AVG(B_{1}):=1+\pi$, but very high worst case cost$WRS(B_{1}):=1+2\pi$.  Motivated by the above, we introduce constrained optimization problem$_2Evac_{F2F}^w$, in which one is trying to minimize the average case cost ofthe evacuation algorithm given that the worst case cost does not exceed $w$.The problem is of special interest with respect to practical applications,since a common objective in search-and-rescue operations is to minimize theaverage completion time, given that a certain worst case threshold is notexceeded, e.g. for safety or limited energy reasons. Our main contribution isthe design and analysis of families of new evacuation parameterized algorithms$A(p)$ which can solve $_2Evac_{F2F}^w$, for every $w \in[WRS(B_{1}),WRS(B_{2})]$.

Average Case - Worst Case Tradeoffs for Evacuating 2 Robots from the Disk in the Face-to-Face Model