Average Case - Worst Case Tradeoffs for Evacuating 2 Robots from the Disk in the Face-to-Face Model
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The problem of evacuating two robots from the disk in the face-to-face model was first introduced in [Czyzowicz et al., DISC'14], and extensively studied (along with many variations) ever since with respect to worst case analysis. We initiate 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] with worst 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 induced worst case cost improvements in subsequent publications has better average case cost, hence concluding that our problem requires the invention of new algorithms. Then, we observe that a remarkable simple algorithm, B_1, has very small average case cost AVG(B_1):=1+π, but very high worst case cost WRS(B_1):=1+2π. Motivated by the above, we introduce constrained optimization problem _2Evac_F2F^w, in which one is trying to minimize the average case cost of the 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 the average completion time, given that a certain worst case threshold is not exceeded, e.g. for safety or limited energy reasons. Our main contribution is the design and analysis of families of new evacuation parameterized algorithms A(p) which can solve _2Evac_F2F^w, for every w ∈ [WRS(B_1),WRS(B_2)].
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