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The state-of-the-art algorithm for computing effective resistance relies on a landmark technique, which involves selecting a node that is easy to reach by all the other nodes as a landmark. The performance of this technique heavily depends on the chosen landmark node. However, in many real-life graphs, it is not always possible to find an easily reachable landmark node, which can significantly hinder the algorithm's efficiency. To overcome this problem, we propose a novel multiple landmarks technique which involves selecting a set of landmark nodes V\n            <jats:sub>l<\/jats:sub>\n            such that the other nodes in the graph can easily reach any one of a landmark node in V\n            <jats:sub>l<\/jats:sub>\n            . Specifically, we first propose several new formulas to compute ER with multiple landmarks, utilizing the concept of Schur complement. These new formulas allow us to pre-compute and maintain several small-sized matrices related to V\n            <jats:sub>l<\/jats:sub>\n            as a compact index. With this powerful index technique, we demonstrate that both single-pair and single-source ER queries can be efficiently answered using a newly-developed V\n            <jats:sub>l<\/jats:sub>\n            -absorbed random walk sampling or V\n            <jats:sub>l<\/jats:sub>\n            -absorbed push technique. Comprehensive theoretical analysis shows that all proposed index-based algorithms achieve provable performance guarantees for both single-pair and single-source ER queries. Extensive experiments on 5 real-life datasets demonstrate the high efficiency of our multiple landmarks-based index techniques. For instance, our algorithms, with a 1.5 GB index size, can be up to 4 orders of magnitude faster than the state-of-the-art algorithms while achieving the same accuracy on a large road network.\n          <\/jats:p>","DOI":"10.1145\/3654936","type":"journal-article","created":{"date-parts":[[2024,5,30]],"date-time":"2024-05-30T09:44:53Z","timestamp":1717062293000},"page":"1-27","source":"Crossref","is-referenced-by-count":3,"title":["Efficient and Provable Effective Resistance Computation on Large Graphs: An Index-based Approach"],"prefix":"10.1145","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5808-3131","authenticated-orcid":false,"given":"Meihao","family":"Liao","sequence":"first","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0303-4902","authenticated-orcid":false,"given":"Junjie","family":"Zhou","sequence":"additional","affiliation":[{"name":"Beijing Institude of technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8658-6599","authenticated-orcid":false,"given":"Rong-Hua","family":"Li","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8569-6558","authenticated-orcid":false,"given":"Qiangqiang","family":"Dai","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7626-0162","authenticated-orcid":false,"given":"Hongyang","family":"Chen","sequence":"additional","affiliation":[{"name":"Zhejiang Lab, Zhejiang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0181-8379","authenticated-orcid":false,"given":"Guoren","family":"Wang","sequence":"additional","affiliation":[{"name":"Beijing Institute of Technology, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,5,30]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-55699-4_26"},{"key":"e_1_2_1_2_1","volume-title":"Muhammad Aamir Cheema, and David Taniar","author":"Abeywickrama Tenindra","year":"2016","unstructured":"Tenindra Abeywickrama, Muhammad Aamir Cheema, and David Taniar. 2016. k-Nearest Neighbors on Road Networks: A Journey in Experimentation and In-Memory Implementation. 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