{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T01:36:35Z","timestamp":1761183395729,"version":"build-2065373602"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62162021","62462028","62362026"],"award-info":[{"award-number":["62162021","62462028","62362026"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hainan Provincial Natural Science Foundation of China","award":["623RC448"],"award-info":[{"award-number":["623RC448"]}]},{"name":"Innovation Platform for Academicians of Hainan Province","award":["YSPTZX202314"],"award-info":[{"award-number":["YSPTZX202314"]}]},{"name":"Haikou Science and Technology Plan Project","award":["2023-055"],"award-info":[{"award-number":["2023-055"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>With the increment of the scale of data centers, device failures are inevitable, which requires high reliability of underlying network. Recursively defined structures can construct large-scale and high-performance data center networks (DCNs), where the investigation of reliability in this group of structures is insufficient as in the representative DPCell. In this paper, a comprehensive research on reliability of DPCell structure was carried out, including the diagnosability based on precise and pessimistic diagnostic strategies, $h$-extra connectivity, and $h$-extra conditional diagnosability. Let $r$ denote the number of layers in a DPCell structure. Let $k_{i}$ denote the degree used to connect to a vertex in the $i$th layer with $0 \\leq i \\leq r$. Let $h$ denote a scalar, where each connected component contains at least $h+1$ vertices in $G-F$. This research proves that (i) under the precise diagnosis strategy, ${DPCell}_{r}$ is $\\sum _{i=0}^{r}k_{i}$-diagnosable for $r\\geq 2$; (ii) under the pessimistic diagnosis strategy, ${DPCell}_{r}$ is $\\left(\\frac{k_{0}-1}{2}\\right)\/\\left(\\frac{k_{0}-1}{2}\\right)$-diagnosable and $(\\sum _{i=1}^{r}k_{i}-1)\/(\\sum _{i=1}^{r}k_{i}-1)$-diagnosable for $r\\geq 0$; (iii) the $h$-extra connectivity $\\kappa _{h}({DPCell}_{r})=(h+1)(\\sum _{i=1}^{r}k_{i}-1)+k_{0}+1$ for $r\\geq 1$ and $0\\le h\\le k_{0}$; and (iv) the $h$-extra conditional diagnosability $\\widetilde{t_{h}^{P}}({DPCell}_{r})=(h+1)\\sum _{i=1}^{r}k_{i}+k_{0}$ for $r\\geq 2$ and $0\\le h\\le k_{0}$. Based on the research of connectivity and diagnosability, the reliability of DPCell structure can be evaluated quantitatively. This research results in a comprehensive understanding of the reliability of DPCell, which contributes to network performance improvement of recursively defined structures.<\/jats:p>","DOI":"10.1093\/comjnl\/bxaf058","type":"journal-article","created":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T07:47:17Z","timestamp":1748591237000},"page":"1555-1564","source":"Crossref","is-referenced-by-count":0,"title":["Research on Reliability of DPCell structure"],"prefix":"10.1093","volume":"68","author":[{"given":"Deshun","family":"Li","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology , Hainan University, No. 58, Renmin Avenue, Meilan District, Haikou, Hainan Province, 570228,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinlong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology , Hainan University, No. 58, Renmin Avenue, Meilan District, Haikou, Hainan 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