2 research outputs found
Optimally Sorting Evolving Data
We give optimal sorting algorithms in the evolving data framework, where an algorithm\u27s input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an output close to the correct output for the current state of the data, repeatedly updating its best estimate of a correct output over time. We show that a simple repeated insertion-sort algorithm can maintain an O(n) Kendall tau distance, with high probability, between a maintained list and an underlying total order of n items in an evolving data model where each comparison is followed by a swap between a random consecutive pair of items in the underlying total order. This result is asymptotically optimal, since there is an Omega(n) lower bound for Kendall tau distance for this problem. Our result closes the gap between this lower bound and the previous best algorithm for this problem, which maintains a Kendall tau distance of O(n log log n) with high probability. It also confirms previous experimental results that suggested that insertion sort tends to perform better than quicksort in practice
Tracking Evolving labels using Cone based Oracles
The evolving data framework was first proposed by Anagnostopoulos et al.,
where an evolver makes small changes to a structure behind the scenes. Instead
of taking a single input and producing a single output, an algorithm
judiciously probes the current state of the structure and attempts to
continuously maintain a sketch of the structure that is as close as possible to
its actual state. There have been a number of problems that have been studied
in the evolving framework including our own work on labeled trees. We were
motivated by the problem of maintaining a labeling in the plane, where updating
the labels require physically moving them. Applications involve tracking
evolving disease hot-spots via mobile testing units , and tracking unmanned
aerial vehicles. To be specific, we consider the problem of tracking labeled
nodes in the plane, where an evolver continuously swaps labels of any two
nearby nodes in the background unknown to us. We are tasked with maintaining a
hypothesis, an approximate sketch of the locations of these labels, which we
can only update by physically moving them over a sparse graph. We assume the
existence of an Oracle, which when suitably probed, guides us in fixing our
hypothesis.Comment: This is an abstract of a presentation given at CG:YRF 2023. It has
been made public for the benefit of the community and should be considered a
preprint rather than a formally reviewed paper. Thus, this work is expected
to appear in a conference with formal proceedings and/or in a journa