s side becomes $\\gamma_{uv} \\theta$ units of flow on the $v
th side. In the online problem, there is one sink, and sources come one by one. Upon arrival of a source, we need to send 1 unit flow from the source. A recourse occurs if we change the flow value of an edge. We give an online algorithm for the problem with recourse at most $O(1\u002F\\epsilon)$ times the optimum cost for the instance with capacities scaled by $\\frac{1}{1+\\epsilon}$. The $(1+\\epsilon)$-factor improves upon the corresponding $(2+\\epsilon)$-factor of [GKS14], which only works for the ordinary network flow problem. As an immediate corollary, we also give an improved algorithm for the online $b$-matching problem with reassignment costs. ","authors":[{"id":"53f4312adabfaedd74d67049","name":"Ravishankar Krishnaswamy","org":"Microsoft Research, India","orgs":["Microsoft Research, India"]},{"id":"560600e545cedb339677bb15","name":"Shi Li","org":"University at Buffalo, USA","orgid":"5f71b2a91c455f439fe3d577","orgs":["University at Buffalo, USA"]},{"id":"6523e74655b3f8ac462c88ea","name":"Varun Suriyanarayana","org":"Cornell University, USA","orgid":"5f71b3b11c455f439fe449fb","orgs":["Cornell University, USA"]}],"create_time":"2022-11-30T04:51:28.156Z","hashs":{"h1":"oulbg","h3":"fr"},"id":"6386c9e790e50fcafdfa105b","lang":"en","num_citation":2,"pages":{"end":"788","start":"775"},"pdf":"https:\u002F\u002Fcz5waila03cyo0tux1owpyofgoryroob.aminer.cn\u002F54\u002F85\u002F8C\u002F54858C1093403AE72D9BE1EFE462087E.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2211.16216"],"title":"Online Unrelated-Machine Load Balancing and Generalized Flow with\n Recourse","update_times":{"u_a_t":"2022-11-30T22:50:15.007Z"},"urls":["db\u002Fconf\u002Fstoc\u002Fstoc2023.html#Krishnaswamy0S23","https:\u002F\u002Fdoi.org\u002F10.1145\u002F3564246.3585222","http:\u002F\u002Facm-stoc.org\u002Fstoc2023\u002Faccepted.html","https:\u002F\u002Fdl.acm.org\u002Fdoi\u002F10.1145\u002F3564246.3585222","https:\u002F\u002Farxiv.org\u002Fabs\u002F2211.16216"],"versions":[{"id":"6386c9e790e50fcafdfa105b","sid":"2211.16216","src":"arxiv","year":2022},{"id":"6475a831d68f896efa9091f5","sid":"10.1145\u002F3564246.3585222","src":"acm","year":2023},{"id":"64b63a723fda6d7f0642273f","sid":"stoc2023#124","src":"conf_stoc","year":2023},{"id":"6479e3add68f896efa4e7aab","sid":"conf\u002Fstoc\u002FKrishnaswamy0S23","src":"dblp","year":2023}],"year":2022},{"abstract":" Approximate nearest neighbor search (ANNS) is a fundamental building block in information retrieval with graph-based indices being the current state-of-the-art and widely used in the industry. Recent advances in graph-based indices have made it possible to index and search billion-point datasets with high recall and millisecond-level latency on a single commodity machine with an SSD. However, existing graph algorithms for ANNS support only static indices that cannot reflect real-time changes to the corpus required by many key real-world scenarios (e.g. index of sentences in documents, email, or a news index). To overcome this drawback, the current industry practice for manifesting updates into such indices is to periodically re-build these indices, which can be prohibitively expensive. In this paper, we present the first graph-based ANNS index that reflects corpus updates into the index in real-time without compromising on search performance. Using update rules for this index, we design FreshDiskANN, a system that can index over a billion points on a workstation with an SSD and limited memory, and support thousands of concurrent real-time inserts, deletes and searches per second each, while retaining $\u003E95\\%$ 5-recall@5. This represents a 5-10x reduction in the cost of maintaining freshness in indices when compared to existing methods. ","authors":[{"name":"Aditi Singh"},{"name":"Suhas Jayaram Subramanya"},{"id":"53f4312adabfaedd74d67049","name":"Ravishankar Krishnaswamy"},{"id":"53f4d6f5dabfaef55af80b20","name":"Harsha Vardhan Simhadri"}],"create_time":"2021-05-21T14:38:27.649Z","hashs":{"h1":"ffaga","h3":"isss"},"id":"60a78fb191e011f90a51ddb1","num_citation":0,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F21\u002F2105\u002F2105.09613.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2105.09613"],"title":"FreshDiskANN: A Fast and Accurate Graph-Based ANN Index for Streaming Similarity Search","urls":["db\u002Fjournals\u002Fcorr\u002Fcorr2105.html#abs-2105-09613","https:\u002F\u002Farxiv.org\u002Fabs\u002F2105.09613"],"versions":[{"id":"60a78fb191e011f90a51ddb1","sid":"2105.09613","src":"arxiv","year":2021},{"id":"6456479ad68f896efae2f12d","sid":"journals\u002Fcorr\u002Fabs-2105-09613","src":"dblp","year":2021}],"year":2021},{"abstract":"Despite the broad range of algorithms for Approximate Nearest Neighbor Search, most empirical evaluations of algorithms have focused on smaller datasets, typically of 1 million points \\citep{Benchmark}. However, deploying recent advances in embedding based techniques for search, recommendation and ranking at scale require ANNS indices at billion, trillion or larger scale. Barring a few recent papers, there is limited consensus on which algorithms are effective at this scale vis-à-vis their hardware cost. This competition\\footnote{\\url{https:\u002F\u002Fbig-ann-benchmarks.com}} compares ANNS algorithms at billion-scale by hardware cost, accuracy and performance. We set up an open source evaluation framework\\footnote{\\url{https:\u002F\u002Fgithub.com\u002Fharsha-simhadri\u002Fbig-ann-benchmarks\u002F}}% and leaderboards for both standardized and specialized hardware. The competition involves three tracks. The standard hardware track T1 evaluates algorithms on an Azure VM with limited DRAM, often the bottleneck in serving billion-scale indices, where the embedding data can be hundreds of GigaBytes in size. It uses FAISS \\citep{Faiss17} as the baseline. The standard hardware track T2 additional allows inexpensive SSDs in addition to the limited DRAM and uses DiskANN \\citep{DiskANN19} as the baseline. The specialized hardware track T3 allows any hardware configuration, and again uses FAISS as the baseline. We compiled six diverse billion-scale datasets, four newly released for this competition, that span a variety of modalities, data types, dimensions, deep learning models, distance functions and sources. The outcome of the competition was ranked leaderboards of algorithms in each track based on recall at a query throughput threshold. Additionally, for track T3, separate leaderboards were created based on recall as well as cost-normalized and power-normalized query throughput.","authors":[{"id":"53f4d6f5dabfaef55af80b20","name":"Harsha Vardhan Simhadri"},{"id":"53f472a9dabfaec09f26f0e8","name":"George Williams"},{"id":"64cc9f6b70d44317c2e3a76f","name":"Martin Aumüller"},{"id":"53f42febdabfaee0d9b1ccee","name":"Matthijs Douze"},{"id":"53f439a6dabfaec22ba9f755","name":"Artem Babenko"},{"id":"53f44cacdabfaefedbb2c7d3","name":"Dmitry Baranchuk"},{"id":"53f43daedabfaedce55661bd","name":"Qi Chen"},{"id":"637277dfec88d95668ce5c75","name":"Lucas Hosseini"},{"id":"53f4312adabfaedd74d67049","name":"Ravishankar Krishnaswamy"},{"id":"63772bd184d6908c16ae832f","name":"Gopal Srinivasa"},{"id":"61830c858672f1a6df29481f","name":"Suhas Jayaram Subramanya"},{"id":"53f431c1dabfaee43ebfd72a","name":"Jingdong Wang"}],"citations":{"google_citation":0,"last_citation":0},"create_time":"2022-05-10T02:45:18.498Z","hashs":{"h1":"rncba","h3":"nns"},"id":"6279c9c55aee126c0fdadd27","lang":"en","num_citation":0,"pages":{"end":"189","start":"177"},"pdf":"https:\u002F\u002Fcz5waila03cyo0tux1owpyofgoryroob.aminer.cn\u002F3C\u002F3F\u002F7B\u002F3C3F7B9A8B2B04518206DA462769A520.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2205.03763"],"title":"Results of the NeurIPS'21 Challenge on Billion-Scale Approximate Nearest Neighbor Search.","update_times":{"u_a_t":"2022-08-19T03:14:42.121Z","u_c_t":"2023-10-13T10:32:06.15Z","u_v_t":"2022-08-18T15:11:40.755Z"},"urls":["https:\u002F\u002Fproceedings.mlr.press\u002Fv176\u002Fsimhadri22a.html","https:\u002F\u002Farxiv.org\u002Fabs\u002F2205.03763"],"venue":{"info":{"name":"Annual Conference on Neural Information Processing Systems","name_s":"NeurIPS","publisher":"dblp"},"lang":"en","type":2},"venue_hhb_id":"5ea1e340edb6e7d53c011a4c","versions":[{"id":"6279c9c55aee126c0fdadd27","sid":"2205.03763","src":"arxiv","year":2022},{"id":"62fe164c90e50fcafd9fa07b","sid":"conf\u002Fnips\u002FSimhadriWADBBCH21","src":"dblp","vsid":"conf\u002Fnips","year":2021}],"year":2021},{"abstract":" We consider the online carpooling problem: given $n$ vertices, a sequence of edges arrive over time. When an edge $e_t = (u_t, v_t)$ arrives at time step $t$, the algorithm must orient the edge either as $v_t \\rightarrow u_t$ or $u_t \\rightarrow v_t$, with the objective of minimizing the maximum discrepancy of any vertex, i.e., the absolute difference between its in-degree and out-degree. Edges correspond to pairs of persons wanting to ride together, and orienting denotes designating the driver. The discrepancy objective then corresponds to every person driving close to their fair share of rides they participate in. In this paper, we design efficient algorithms which can maintain polylog$(n,T)$ maximum discrepancy (w.h.p) over any sequence of $T$ arrivals, when the arriving edges are sampled independently and uniformly from any given graph $G$. This provides the first polylogarithmic bounds for the online (stochastic) carpooling problem. Prior to this work, the best known bounds were $O(\\sqrt{n \\log n})$-discrepancy for any adversarial sequence of arrivals, or $O(\\log\\!\\log n)$-discrepancy bounds for the stochastic arrivals when $G$ is the complete graph. The technical crux of our paper is in showing that the simple greedy algorithm, which has provably good discrepancy bounds when the arriving edges are drawn uniformly at random from the complete graph, also has polylog discrepancy when $G$ is an expander graph. We then combine this with known expander-decomposition results to design our overall algorithm. ","authors":[{"id":"53f442b4dabfaeb22f4b249d","name":"Anupam Gupta","org":"Carnegie Mellon University","orgid":"5f71b2861c455f439fe3c771","orgs":["Carnegie Mellon University"]},{"id":"53f4312adabfaedd74d67049","name":"Ravishankar Krishnaswamy","org":"Microsoft","orgid":"5f71b2831c455f439fe3c634","orgs":["Microsoft"]},{"id":"560dab6d45ce1e5960e81e86","name":"Amit Kumar","org":"Indian Institute of Technology Delhi","orgid":"5f71b3dc1c455f439fe45dfa","orgs":["Indian Institute of Technology Delhi"]},{"id":"5625676b45ce1e5964e7ff2e","name":"Sahil Singla","org":"Princeton University","orgid":"5f71b2831c455f439fe3c663","orgs":["Princeton University"]}],"citations":{"google_citation":1},"create_time":"2020-07-22T13:00:31.5Z","doi":"10.4230\u002FLIPIcs.FSTTCS.2020.23","flags":[{"flag":"affirm_author","person_id":"53f442b4dabfaeb22f4b249d"}],"hashs":{"h1":"oced"},"id":"5f18074291e011c28ff02cc1","num_citation":2,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F20\u002F2007\u002F2007.10545.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F2007.10545"],"title":"Online Carpooling using Expander Decompositions","update_times":{"u_a_t":"2020-07-23T10:34:00.352Z","u_c_t":"2023-03-27T20:40:24.337Z","u_v_t":"2021-01-27T09:44:33.442Z"},"urls":["https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Ffsttcs\u002FGuptaK0020","https:\u002F\u002Fdoi.org\u002F10.4230\u002FLIPIcs.FSTTCS.2020.23","https:\u002F\u002Fdblp.uni-trier.de\u002Fdb\u002Fjournals\u002Fcorr\u002Fcorr2007.html#abs-2007-10545","https:\u002F\u002Farxiv.org\u002Fpdf\u002F2007.10545","db\u002Fjournals\u002Fcorr\u002Fcorr2007.html#abs-2007-10545","https:\u002F\u002Farxiv.org\u002Fabs\u002F2007.10545"],"venue":{"info":{"name":"FSTTCS"},"volume":"abs\u002F2007.10545"},"venue_hhb_id":"5ea1cb6dedb6e7d53c00f5b5","versions":[{"id":"5f18074291e011c28ff02cc1","sid":"2007.10545","src":"arxiv","year":2020},{"id":"5ff8832d91e011c832671fa9","sid":"conf\u002Ffsttcs\u002FGuptaK0020","src":"dblp","vsid":"conf\u002Ffsttcs","year":2020},{"id":"600fe84fd4150a363c241e0b","sid":"3116760519","src":"mag","vsid":"1123496967","year":2020},{"id":"645647add68f896efae3801a","sid":"journals\u002Fcorr\u002Fabs-2007-10545","src":"dblp","year":2020}],"year":2020},{"abstract":" In the classical Online Metric Matching problem, we are given a metric space with $k$ servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The goal is to find an online matching which minimizes the total cost, i.e., the sum of distances between each client and the server it is matched to. We know deterministic algorithms~\\cite{KP93,khuller1994line} that achieve a competitive ratio of $2k-1$, and this bound is tight for deterministic algorithms. The problem has also long been considered in specialized metrics such as the line metric or metrics of bounded doubling dimension, with the current best result on a line metric being a deterministic $O(\\log k)$ competitive algorithm~\\cite{raghvendra2018optimal}. Obtaining (or refuting) $O(\\log k)$-competitive algorithms in general metrics and constant-competitive algorithms on the line metric have been long-standing open questions in this area. In this paper, we investigate the robustness of these lower bounds by considering the Online Metric Matching with Recourse problem where we are allowed to change a small number of previous assignments upon arrival of a new client. Indeed, we show that a small logarithmic amount of recourse can significantly improve the quality of matchings we can maintain. For general metrics, we show a simple \\emph{deterministic} $O(\\log k)$-competitive algorithm with $O(\\log k)$-amortized recourse, an exponential improvement over the $2k-1$ lower bound when no recourse is allowed. We next consider the line metric, and present a deterministic algorithm which is $3$-competitive and has $O(\\log k)$-recourse, again a substantial improvement over the best known $O(\\log k)$-competitive algorithm when no recourse is allowed. ","authors":[{"name":"Gupta Varun","org":"University of Chicago","orgs":["University of Chicago"]},{"id":"53f4312adabfaedd74d67049","name":"Krishnaswamy Ravishankar","org":"Microsoft","orgid":"5f71b2831c455f439fe3c634","orgs":["Microsoft"]},{"id":"61776fc460a9653dc633be6a","name":"Sandeep Sai","org":"Carnegie Mellon University","orgid":"5f71b2861c455f439fe3c771","orgs":["Carnegie Mellon University"]}],"create_time":"2020-04-06T21:53:32.397Z","doi":"10.4230\u002FLIPIcs.APPROX\u002FRANDOM.2020.40","hashs":{"h1":"psbpr","h3":"omm"},"id":"5de4e0bf3a55ac2224ba5491","num_citation":0,"pdf":"https:\u002F\u002Fstatic.aminer.cn\u002Fstorage\u002Fpdf\u002Farxiv\u002F19\u002F1911\u002F1911.12778.pdf","pdf_src":["https:\u002F\u002Farxiv.org\u002Fpdf\u002F1911.12778"],"title":"PERMUTATION Strikes Back: The Power of Recourse in Online Metric Matching","update_times":{"u_a_t":"2020-07-04T07:03:56.434Z","u_v_t":"2021-01-08T22:39:02.543Z"},"urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F1911.12778","https:\u002F\u002Fdblp.uni-trier.de\u002Fdb\u002Fjournals\u002Fcorr\u002Fcorr1911.html#abs-1911-12778","https:\u002F\u002Fui.adsabs.harvard.edu\u002Fabs\u002F2019arXiv191112778G\u002Fabstract","https:\u002F\u002Farxiv.org\u002Fpdf\u002F1911.12778.pdf","https:\u002F\u002Fdblp.org\u002Frec\u002Fconf\u002Fapprox\u002F0004KS20","https:\u002F\u002Fdoi.org\u002F10.4230\u002FLIPIcs.APPROX\u002FRANDOM.2020.40"],"venue":{"info":{"name":"APPROX\u002FRANDOM"}},"venue_hhb_id":"5ebaca78edb6e7d53c104d07","versions":[{"id":"5de4e0bf3a55ac2224ba5491","sid":"1911.12778","src":"arxiv","year":2019},{"id":"5ff6847fd4150a363cbe13d8","sid":"3081862881","src":"mag","vsid":"2757547734","year":2019},{"id":"5ff8846c91e011c832677254","sid":"conf\u002Fapprox\u002F0004KS20","src":"dblp","vsid":"conf\u002Fapprox","year":2020}],"year":2020},{"abstract":"In this article, we introduce and study the Non-Uniform k -Center (NUkC) problem. Given a finite metric space ( X , d ) and a collection of balls of radii { r 1 ≥ … ≥ r k }, the NUkC problem is to find a placement of their centers in the metric space and find the minimum dilation α, such that the union of balls of radius α ⋅ r i around the i th center covers all the points in X . This problem naturally arises as a min-max vehicle routing problem with fleets of different speeds. The NUkC problem generalizes the classic k -center problem, wherein all the k radii are the same (which can be assumed to be 1 after scaling). It also generalizes the k -center with outliers (kCwO for short) problem, in which there are k balls of radius 1 and ℓ (number of outliers) balls of radius 0. Before this work, there was a 2-approximation and 3-approximation algorithm known for these problems, respectively; the former is best possible unless P=NP. We first observe that no O (1)-approximation to the optimal dilation is possible unless P=NP, implying that the NUkC problem is harder than the above two problems. Our main algorithmic result is an ( O (1), O (1))- bi-criteria approximation result: We give an O (1)-approximation to the optimal dilation; however, we may open Θ(1) centers of each radii. Our techniques also allow us to prove a simple (uni-criterion), optimal 2-approximation to the kCwO problem improving upon the long-standing 3-factor approximation for this problem. Our main technical contribution is a connection between the NUkC problem and the so-called firefighter problems on trees that have been studied recently in the TCS community. We show NUkC is at least as hard as the firefighter problem. While we do nt know whether the converse is true, we are able to adapt ideas from recent works [1, 3] in non-trivial ways to obtain our constant factor bi-criteria approximation.","authors":[{"id":"54341d67dabfaeb4c6ae5371","name":"Deeparnab Chakrabarty","org":"Dartmouth College, Hanover, NH, USA","orgid":"5f71b2811c455f439fe3c5c3","orgs":["Dartmouth College, Hanover, NH, USA"]},{"id":"6377987984d6908c16b02986","name":"Prachi Goyal","org":"Microsoft, Redmond, WA USA","orgid":"5f71b2831c455f439fe3c634","orgs":["Microsoft, Redmond, WA USA"]},{"id":"53f4312adabfaedd74d67049","name":"Ravishankar Krishnaswamy","org":"Microsoft Research, Bengaluru, Karnataka, India","orgs":["Microsoft Research, Bengaluru, Karnataka, India"]}],"create_time":"2023-01-24T00:23:49.238Z","doi":"10.1145\u002F3392720","hashs":{"h1":"ncp"},"id":"6219348b5aee126c0fb6b219","issn":"1549-6325","num_citation":0,"pages":{"end":"19","start":"1"},"title":"The Non-Uniform\n \u003Ci\u003Ek\u003C\u002Fi\u003E\n -Center Problem","urls":["http:\u002F\u002Fdx.doi.org\u002F10.1145\u002F3392720"],"venue":{"info":{"name":"ACM Transactions on Algorithms"},"issue":"4","volume":"16"},"venue_hhb_id":"5ea17f53edb6e7d53c0093c5","versions":[{"id":"6219348b5aee126c0fb6b219","sid":"10.1145\u002F3392720","src":"crossref"}],"year":2020}],"profilePubsTotal":57,"profilePatentsPage":0,"profilePatents":null,"profilePatentsTotal":null,"profilePatentsEnd":false,"profileProjectsPage":1,"profileProjects":{"success":true,"msg":"","data":null,"log_id":"2ZOJZIDFEqLxUY3Tz5NNN29QIQO"},"profileProjectsTotal":0,"newInfo":null,"checkDelPubs":[]}};