An algebraic approach to the prefix model analysis of binary trie structures and set intersection algorithms

AbstractThe trie, or digital tree, is a standard data structure for representing sets of strings over a given finite alphabet. Since Knuth's original work (1973), these data structures have been extensively studied and analyzed. In this paper, we present an algebraic approach to the analysis of average storage and average time required by the retrieval algorithms of trie structures under the prefix model. This approach extends the work of Flajolet et al. for other models which, unlike the prefix model, assume that no key in a sample set is the prefix of another. As the main application, we analyze the average running time of two algorithms for computing set intersections

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Annual Reports of the Department of the Interior for the fiscal year ended June 30, 1897; Annual Report of the Commissioner of Education, 1897.

Annual Report of the Sec. of Interior. 16 Nov. HD 5, 55-2, v12-22, 8978p. [3640-3650] Indian affairs; annual report of the Gen. Land Office (Serial 3640); annual report of the CIA (Serial 3641); etc

Maritime expressions:a corpus based exploration of maritime metaphors

This study uses a purpose-built corpus to explore the linguistic legacy of Britain’s maritime history found in the form of hundreds of specialised ‘Maritime Expressions’ (MEs), such as TAKEN ABACK, ANCHOR and ALOOF, that permeate modern English. Selecting just those expressions commencing with ’A’, it analyses 61 MEs in detail and describes the processes by which these technical expressions, from a highly specialised occupational discourse community, have made their way into modern English. The Maritime Text Corpus (MTC) comprises 8.8 million words, encompassing a range of text types and registers, selected to provide a cross-section of ‘maritime’ writing. It is analysed using WordSmith analytical software (Scott, 2010), with the 100 million-word British National Corpus (BNC) as a reference corpus. Using the MTC, a list of keywords of specific salience within the maritime discourse has been compiled and, using frequency data, concordances and collocations, these MEs are described in detail and their use and form in the MTC and the BNC is compared. The study examines the transformation from ME to figurative use in the general discourse, in terms of form and metaphoricity. MEs are classified according to their metaphorical strength and their transference from maritime usage into new registers and domains such as those of business, politics, sports and reportage etc. A revised model of metaphoricity is developed and a new category of figurative expression, the ‘resonator’, is proposed. Additionally, developing the work of Lakov and Johnson, Kovesces and others on Conceptual Metaphor Theory (CMT), a number of Maritime Conceptual Metaphors are identified and their cultural significance is discussed