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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
Complexity of dynamic data structures
 Král, Karel ; Koucký, Michal (advisor) ; Drucker, Andrew (referee) ; Ishai, Yuval (referee)
Sorting is one of the fundamental problems in computer science. In this thesis we present three individual results. Asymptotically optimal sorting networks have been created by Ajtai et al. [1983]. But Asharov et al. [2021] have observed that boolean circuits based on sorting networks are not optimal for sorting short integers. We present a construction of even smaller boolean circuits for sorting short integers. Lower bounds for offline Oblivious RAM have been connected to lower bounds for sorting circuits by Boyle and Naor [2016]. Larsen and Nielsen [2018] have shown a lower bound for online Oblivious RAM. We provide a lower bound for online Oblivious RAM in a more general model. Finally we provide an algorithm with expected running time O(n log log(n)) for sort- ing integers on random access machine with word length between log(n) and log(n) cubed. This algorithm does not match the expected running time of the algorithm of Han and Thorup [2002], but our algorithm is much easier to implement and analyse. 1
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