Rankings: From similarity distances computation to interactive synchronization

Rankings;similarity distance;synchronization;order-optimal

Su, Lili ; Milenkovic ; Olgica

关键词: Rankings;    similarity distance;    synchronization;    order-optimal;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/49447/Lili_Su.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Two problems related to rankings are investigated in this thesis.Wefirst address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social sciences and data storage. The problem may be summarized as follows. Given two rankings and a positive cost function on transpositions that depends on the similarity of the candidates involved, find a smallest cost sequence of transpositions that converts one ranking intoanother. Our focus is on costs that may be described via special metric-tree structures and on full rankings modeled as permutations. The presented results include a quadratic-time algorithm forfinding a minimum cost trans-form for simple cycles; and a linear time, 5/3-approximation algorithm for permutations that contain multiple cycles. In addition, for permutations with digraphs represented by non-intersecting cycles embedded in trees, we present a polynomial-time transform algorithm. The proposed methods rely on investigating a newly introduced balancing property of cycles embedded in trees, cycle-merging methods, and shortest-path optimization techniques.The second problem considered is the problem of exact synchronization of two rankings at remote locations connected by a two-way channel. Such synchronization problems arise when items in the data are distinguishable, as is the case for playlists, tasklists, crowd votes and recommender systems rankings. Our model accounts for differentconstraints on the communicationthroughput of the forward and feedback links, resulting in different anchoring, syndrome and checksum computation strategies. Information editing is assumed of the form of deletions, insertions, block deletions/insertions, translocations and transpositions. The protocols developed under the given model are order-optimal with respect to genie-aided lower bounds.