Statistical properties of a class of randomized binary search algorithms
In this paper, we analyze the statistical properties of a randomized binary search algorithm and its variants. These algorithms have applications in caching and load balancing in distributed environments such as peer-to-peer networks, cloud storage, data centers, and content distribution networks. T...
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| Veröffentlicht in: | Performance evaluation Jg. 168; S. 102478 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.06.2025
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| ISSN: | 0166-5316 |
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| Abstract | In this paper, we analyze the statistical properties of a randomized binary search algorithm and its variants. These algorithms have applications in caching and load balancing in distributed environments such as peer-to-peer networks, cloud storage, data centers, and content distribution networks. The basic discrete version of the problem is as follows. Suppose there are m servers, numbered 1, 2, …, m, out of which the first k servers are marked as special, where k is unknown. These k servers may contain a particular file or service that clients want. The objective is to select one of the marked servers uniformly at random. Considering the intended applications, we impose the constraint that there is no central controller to facilitate the selection process. We start with a basic algorithm: In each step, the client requesting the service chooses a number y uniformly at random from 1,2,…,x, where x is the number chosen in the previous step, initially set to m in the first step. A query is then sent to server y asking whether y is marked. If the answer is yes, the algorithm returns y; otherwise, the process is repeated with x←y. In this paper, we primarily consider two batch versions of this algorithm in which multiple numbers are chosen in each step and multiple queries are made in parallel. We derive the mean and variance (exact and/or asymptotic) for the number of search steps in each version of the algorithm, and when possible, we give its distribution. Additionally, we analyze the access pattern of queries across the entire search space. |
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| AbstractList | In this paper, we analyze the statistical properties of a randomized binary search algorithm and its variants. These algorithms have applications in caching and load balancing in distributed environments such as peer-to-peer networks, cloud storage, data centers, and content distribution networks. The basic discrete version of the problem is as follows. Suppose there are m servers, numbered 1, 2, …, m, out of which the first k servers are marked as special, where k is unknown. These k servers may contain a particular file or service that clients want. The objective is to select one of the marked servers uniformly at random. Considering the intended applications, we impose the constraint that there is no central controller to facilitate the selection process. We start with a basic algorithm: In each step, the client requesting the service chooses a number y uniformly at random from 1,2,…,x, where x is the number chosen in the previous step, initially set to m in the first step. A query is then sent to server y asking whether y is marked. If the answer is yes, the algorithm returns y; otherwise, the process is repeated with x←y. In this paper, we primarily consider two batch versions of this algorithm in which multiple numbers are chosen in each step and multiple queries are made in parallel. We derive the mean and variance (exact and/or asymptotic) for the number of search steps in each version of the algorithm, and when possible, we give its distribution. Additionally, we analyze the access pattern of queries across the entire search space. |
| ArticleNumber | 102478 |
| Author | Xia, Ye |
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| Cites_doi | 10.1109/BigData50022.2020.9378465 10.1016/j.peva.2014.07.003 10.1145/1842733.1842736 10.1016/j.peva.2020.102151 10.1145/2254756.2254766 10.1145/383059.383071 10.1145/2390021.2390028 10.1016/j.peva.2017.08.004 10.1016/j.peva.2020.102146 10.1016/j.peva.2024.102408 10.1145/258533.258660 |
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| Keywords | Distributed search Randomized binary search algorithm Analysis of algorithms Parallel and distributed algorithms Load balancing |
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| SubjectTerms | Analysis of algorithms Distributed search Load balancing Parallel and distributed algorithms Randomized binary search algorithm |
| Title | Statistical properties of a class of randomized binary search algorithms |
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