[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86119-en":3,"doc-seo-86119-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86119,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Continuous Query for Top K Maximal Sum Intervals over Streaming Data","Continuous identification of the top-K maximal sum intervals over a sliding window streaming model enables real-time analytics in IoT and related domains. A maximal sum interval is defined as a nonoverlapping, contiguous subsequence whose sum is maximal among signed numeric values. Existing methods are inefficient for streaming, either enumerating many intervals for small K or relying on costly reindexing. The work proposes a partition-based strategy that guarantees each maximal interval lies within one partition, supporting pruning, parallel processing, and incremental maintenance with improved efficiency on real and synthetic data.","Continuous Query for Top-􀀠 Maximal Sum Intervals over  \nStreaming Data  \nZhongshuai Zhang Beijing Institute of Technology [zhang_zhongshuai@126.com](zhang_zhongshuai@126.com)  \nRui Zhu  \nShenyang Aerospace University [zhurui@sau.edu.cn](zhurui@sau.edu.cn)  \nXiaochun Yang Northeastern University [yangxc@mail.neu.edu.cn](yangxc@mail.neu.edu.cn)  \nHaomin Li Northeastern University [lihm@mails.neu.edu.cn](lihm@mails.neu.edu.cn)  \nBaihua Zheng  \nSingapore Management University [bhzheng@smu.edu.sg](bhzheng@smu.edu.sg)  \nBin Wang Northeastern University [binwang@mail.neu.edu.cn](binwang@mail.neu.edu.cn)  \narXiv :2607 . 11035v1 [ cs .DB] 13 Jul 2026  \nABSTRACT  \nThe continuous identification of top-􀀺 maximal sum intervals using a sliding window over a data stream is a critical operation for applications in IoT and beyond. A maximal sum interval is a nonoverlapping, contiguous subsequence with the maximal sum ina sequence of signed values. Existing algorithms are ill-suited for streaming contexts: they either exhaustively enumerate all intervalseven for small 􀀺 values, or depend on indexes that require frequent and costly restructuring. We propose a novel partition-based strategy. Our core insight is a partitioning scheme that guarantees that any maximal sum interval is fully contained within a single partition, enabling independent and parallel processing. This design provides two key advantages: it enables safe pruning of partitions that cannot contribute to top-􀀺 results, drastically narrowing the search space, and it enables efficient, incremental maintenance of the maximal sum intervals in each partition. We develop algorithms for partition construction, incremental partition updates, and partition-based top-􀀺 maximal sum interval search. Extensive experiments on real and synthetic datasets demonstrate that our approach significantly improves efficiency.  \nPVLDB Reference Format:  \nZhongshuai Zhang, Xiaochun Yang, Baihua Zheng, Rui Zhu, Haomin Li, and Bin Wang. Continuous Query for Top-􀀠 Maximal Sum Intervals over Streaming Data. PVLDB, 19(9): 2289-2302, 2026 .  \ndoi:10.14778/3819518.3819551  \nPVLDB Artifact Availability:  \nThe source code, data, and/or other artifacts have been made available at [https://github.com/zhangzhongshuai/C-KMaxI-code](https://github.com/zhangzhongshuai/C-KMaxI-code).  \n1 INTRODUCTION  \nThe Top-􀀺 Maximal Sum Intervals (KMaxI) problem [6, 26], a classic problem studied for over 25 years, aims to find the 􀀺 nonoverlapping, contiguous subsequences with the highest sums ina sequence of real numbers. These intervals are ranked such that the 􀀸-th interval has the maximum possible sum from the elements  \nThis paper has been accepted by VLDB 2026 .  \nThis work is licensed under the Creative Commons BY-NC-ND 4.0 International License. Visit [https://creativecommons.org/licenses/by-nc-nd/4.0/ to view a copy of](https://creativecommons.org/licenses/by-nc-nd/4.0/ to view a copy of)[ ](https://creativecommons.org/licenses/by-nc-nd/4.0/ to view a copy of)[this license. For any use beyond those covered by this license](this license. For any use beyond those covered by this license), [obtain permission by](obtain permission by)[emailing info@vldb.org. Copyright](emailing info@vldb.org. Copyright) is held by the owner/author(s). Publication rights licensed to the VLDB Endowment.  \nProceedings of the VLDB Endowment, Vol. 19, No. 9 ISSN 2150-8097 .  \ndoi:10.14778/3819518.3819551  \n\n|  | 1 |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| Sample ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ... |\n| Generation | 69.5 | 75.2 | 63.4 | 76.5 | 69.4 | 84.6 | 62.1 | 73.7 | 64.8 | 72.6 | ... |\n| Consumption | 67.7 | 72.8 | 66.6 | 72.7 | 73.4 | 80.7 | 68.6 | 67.9 | 70.1 | 67.9 | ... |\n| Surplus/Deficit* | [1.8 | 2.4 | -3.2 | 3.8] | -4.0 | 3.9 | -6.5 | 5.8 | -5.3 | 4.7 | ... |\n|  |  |  |  |  |  |  |  |  |  |  |  |\n\nUNIT: W 2  \nkWh W  \n11  \n70.4  \n69.2  \n1.2  \nThe 2nd-ranked in","cbCaicOQDOcT30Md","https://ap.wps.com/l/cbCaicOQDOcT30Md","pdf",1846137,4,1,14,"English","en",105,"# Introduction\n## Motivations and Challenges\n# Continuous KMaxI Query Model\n## Sliding Window and Query Semantics\n# Partition-Based Strategy\n## Partition Construction and Incremental Updates\n## Partition-Based Top-K Interval Search\n# Experimental Evaluation","[{\"question\":\"What problem does the Continuous KMaxI query solve?\",\"answer\":\"It continuously monitors the most recent values in a sliding window and returns the top-K maximal sum intervals after each window shift.\"},{\"question\":\"How is a maximal sum interval defined in this work?\",\"answer\":\"It is a nonoverlapping, contiguous subsequence whose sum is maximal among signed numeric values in the sequence, and the returned intervals are ranked.\"},{\"question\":\"Why are existing algorithms unsuitable for streaming data?\",\"answer\":\"They either exhaustively enumerate intervals (even for small K) or depend on indexes that require frequent and costly restructuring, making them inefficient under streaming updates.\"}]",1784208627,35,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"continuous-query-for-top-k-maximal-sum-intervals-over-streaming-data","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/continuous-query-for-top-k-maximal-sum-intervals-over-streaming-data/86119/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the Continuous KMaxI query solve?","Question",{"text":75,"@type":76},"It continuously monitors the most recent values in a sliding window and returns the top-K maximal sum intervals after each window shift.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is a maximal sum interval defined in this work?",{"text":80,"@type":76},"It is a nonoverlapping, contiguous subsequence whose sum is maximal among signed numeric values in the sequence, and the returned intervals are ranked.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are existing algorithms unsuitable for streaming data?",{"text":84,"@type":76},"They either exhaustively enumerate intervals (even for small K) or depend on indexes that require frequent and costly restructuring, making them inefficient under streaming 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