Faster Dynamic Range Mode
In the dynamic range mode problem, we are given a sequence $a$ of length bounded by $N$ and asked to support element insertion, deletion, and queries for the most frequent element of a contiguous subsequence of $a$. In this work, we devise a deterministic data structure that handles each operation i...
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| creator | Sandlund, Bryce Xu, Yinzhan |
| description | In the dynamic range mode problem, we are given a sequence $a$ of length
bounded by $N$ and asked to support element insertion, deletion, and queries
for the most frequent element of a contiguous subsequence of $a$. In this work,
we devise a deterministic data structure that handles each operation in
worst-case $\tilde{O}(N^{0.655994})$ time, thus breaking the $O(N^{2/3})$
per-operation time barrier for this problem. The data structure is achieved by
combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a
novel data structure variant of the Min-Plus product. |
| doi_str_mv | 10.48550/arxiv.2004.08777 |
| format | Article |
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bounded by $N$ and asked to support element insertion, deletion, and queries
for the most frequent element of a contiguous subsequence of $a$. In this work,
we devise a deterministic data structure that handles each operation in
worst-case $\tilde{O}(N^{0.655994})$ time, thus breaking the $O(N^{2/3})$
per-operation time barrier for this problem. The data structure is achieved by
combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a
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bounded by $N$ and asked to support element insertion, deletion, and queries
for the most frequent element of a contiguous subsequence of $a$. In this work,
we devise a deterministic data structure that handles each operation in
worst-case $\tilde{O}(N^{0.655994})$ time, thus breaking the $O(N^{2/3})$
per-operation time barrier for this problem. The data structure is achieved by
combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a
novel data structure variant of the Min-Plus product.</description><subject>Computer Science - Data Structures and Algorithms</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzs0KgkAYheHZtAjrAlzlDWgzzu-3DMsKiiDcy-jMhJAWY0TefWWtzubl8CAUEpwwxTleav9qnkmKMUuwklJOUZjr_mF9tB463TZ1dNbdxUbHm7EzNHH62tv5fwNU5Jsi28WH03afrQ6xFlLGQIGp1JoKjKi5Zooq50zKiKPSVcwBJnUlwVDgDANWIAQ1jHBFKTjxqQK0-N2OtvLum1b7ofway9FI30bhM-Y</recordid><startdate>20200419</startdate><enddate>20200419</enddate><creator>Sandlund, Bryce</creator><creator>Xu, Yinzhan</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20200419</creationdate><title>Faster Dynamic Range Mode</title><author>Sandlund, Bryce ; Xu, Yinzhan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-939482edb9d6c5a4838ffd241f37fb4f901cb79d395409089663d4158339f61f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Data Structures and Algorithms</topic><toplevel>online_resources</toplevel><creatorcontrib>Sandlund, Bryce</creatorcontrib><creatorcontrib>Xu, Yinzhan</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Sandlund, Bryce</au><au>Xu, Yinzhan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Faster Dynamic Range Mode</atitle><date>2020-04-19</date><risdate>2020</risdate><abstract>In the dynamic range mode problem, we are given a sequence $a$ of length
bounded by $N$ and asked to support element insertion, deletion, and queries
for the most frequent element of a contiguous subsequence of $a$. In this work,
we devise a deterministic data structure that handles each operation in
worst-case $\tilde{O}(N^{0.655994})$ time, thus breaking the $O(N^{2/3})$
per-operation time barrier for this problem. The data structure is achieved by
combining the ideas in Williams and Xu (SODA 2020) for batch range mode with a
novel data structure variant of the Min-Plus product.</abstract><doi>10.48550/arxiv.2004.08777</doi><oa>free_for_read</oa></addata></record> |
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| identifier | DOI: 10.48550/arxiv.2004.08777 |
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| subjects | Computer Science - Data Structures and Algorithms |
| title | Faster Dynamic Range Mode |
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