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| 研究生： |
林沂政 Lin, Yi-Jheng |
|---|---|
| 論文名稱： |
多通道交會問題及池化檢測之應用 Multichannel Rendezvous Problem and Its Applications to Pooled Testing |
| 指導教授： |
張正尚
Chang, Cheng-Shang |
| 口試委員: |
陳文村
Chen, Wen-Tsuen 楊谷章 Yang, Guu-Chang 張貴雲 Chang, Guey-Yun 許健平 Sheu, Jang-Ping |
| 學位類別： |
博士 Doctor |
| 系所名稱： |
電機資訊學院 - 通訊工程研究所 Communications Engineering |
| 論文出版年： | 2022 |
| 畢業學年度： | 110 |
| 語文別： | 英文 |
| 論文頁數： | 143 |
| 中文關鍵詞： | 多通道交會問題 、最壞情況分析 、物聯網 、完全差集 、理想矩陣 、有限投影平面 、COVID-19 、池化檢驗 、群試 、再生過程 、馬可夫調變過程 、社群網路 |
| 外文關鍵詞： | multichannel rendezvous problem, worst case analysis, Internet of things, perfect difference sets, ideal matrices, finite projective planes, COVID-19, pooled testing, group testing, regenerative processes, Markov modulated processes, social networks |
| 相關次數： | 點閱：2 下載：0 |
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多通道交會問題是感知無線電網路中的一個基本問題，其問題為設計跳頻序列使二個次要用戶在二者共同可使用通道中交會。已知在具有N個通道的感知無線電網路中，能達到最大交會維度（maximum rendezvous diversity）之跳頻序列的週期至少為N^2。在過去的文獻中，最佳的漸進近似比（其定義為當通道個數N趨近無窮大時，跳頻序列的週期與理論值下界N^2的比值）仍是2.5。多通道交會問題中的一個猜想為：是否能建造出漸進近似比為1的週期性跳頻序列？
在本論文中，我們提出了跳頻序列IDEAL-CH，其漸進近似比為2，此結果為目前文獻上與理論值下界最接近的跳頻序列。若考慮較弱的條件，即二個用戶在一個週期內只需在一個共同可使用通道中交會，我們提出跳頻序列ORTHO-CH，其週期為(2p+1)p，其中p是不小於N的最小質數。
此外，我們從另一個角度討論多通道交會問題中的猜想。我們考慮能達到近乎最大交會維度（nearly full rendezvous diversity）的週期性跳頻序列。我們提出了跳頻序列PPoL。對於具有N個通道的感知無線電網路，當N-1為質數的次方時，跳頻序列PPoL的週期為N^2-N+1，且二個非同步的用戶可相遇的通道數目至少為N-2個。當N+1為質數的次方，且二個用戶的共同可使用通道至少為二個時，我們可以藉由通道再映射建造出最大交會時間（maximum time-to-rendezvous, MTTR）上界為N^2+3N+3的跳頻序列。與過去文獻中最佳的結果相比，此結果在對稱用戶、非同步時間及異質通道的環境中可以減少50%的最大交會時間上界。
我們將多通道交會問題應用於池化檢驗。與個別檢驗相比，池化檢驗能顯著降低檢驗成本，在近期因COVID-19大量檢驗的需求引起了很大的研究興趣。
在本論文中，我們利用PPoL演算法設計出一種新的池化檢驗矩陣。我們比較PPoL池化檢驗矩陣及文獻中不同的池化檢驗矩陣的表現。數值模擬的結果顯示：在盛行率5%內，不存在一個具有最低相對成本的池化檢驗矩陣。因此，對於不同的盛行率，我們應該選用一個適合的池化檢驗矩陣，藉以達到最佳的表現。我們提出的PPoL池化檢驗矩陣能根據不同的盛行率調整演算法中的參數，進而達到最低的相對成本。這會是一個比使用固定的池化檢驗矩陣更好的選擇。
我們更進一步探討混合在同一池中的樣本之間的正相關性。我們證明，當同一池中的樣本具有正相關性時，利用Dorfman二階段演算法能再降低檢驗成本。最後，我們提出一個能在社群網路上做池化檢驗的聚合式階層演算法，其中此社群網路的鏈結代表兩個節點之間有頻繁的社交接觸。使用Dorfman二階段演算法，此聚合式階層演算法可以比隨機混合的方式減少約20%–35%的檢驗成本。
The multichannel rendezvous problem, which asks two secondary users to meet each other by hopping over their available channels, is a fundamental problem in cognitive radio networks (CRNs). It is known that the period of a channel hopping (CH) sequence that achieves maximum rendezvous diversity is at least N^2 for a CRN with N channels. The asymptotic approximation ratio, defined as the ratio of the period of a CH sequence to the lower bound N^2 when N→∞, is still 2.5 for the best known CH sequence in the literature. A conjecture in the multichannel rendezvous problem is whether it is possible to construct a periodic CH sequence with an asymptotic approximation ratio of 1.
In this dissertation, we tighten the theoretical gap by proposing CH sequences, called IDEAL-CH, with an asymptotic approximation ratio of 2. To the best of our knowledge, this is the best asymptotic approximation ratio in the literature. For a weaker requirement that only needs the two users to rendezvous on one commonly available channel in a period, we propose channel hopping sequences, called ORTHO-CH, with period (2p+1)p, where p is the smallest prime not less than N.
Furthermore, we tackle the conjecture from another perspective by considering periodic CH sequences with nearly full rendezvous diversity. We propose a CH sequence called PPoL. For a CRN with N channels, when N-1 is a prime power, the period of PPoL is N^2-N+1, and the number of distinct rendezvous channels of PPoL is at least N-2 for any nonzero clock drift. When N+1 is a prime power, we further demonstrate by channel remapping that one can construct CH sequences with the maximum time-to-rendezvous (MTTR) bounded by N^2+3N+3 if the number of commonly available channels is at least two. This achieves a roughly 50% reduction of the state-of-the-art MTTR bound in the symmetric, asynchronous, and heterogeneous setting of the multichannel rendezvous problem.
We consider pooled testing as an application of the multichannel rendezvous problem. The pooled testing approach, which achieves significant cost reduction over the individual testing approach, has received a lot of interest lately for massive testing of COVID-19.
In this dissertation, we apply the PPoL algorithm to construct a new family of pooling matrices. We compare their performance with various pooling matrices proposed in the literature. By conducting extensive simulations for a range of prevalence rates up to 5%, our numerical results indicate no pooling matrix with the lowest relative cost in the whole range of the prevalence rates. Therefore, one should choose a suitable pooling matrix to optimize the performance depending on the prevalence rate. The family of PPoL matrices can dynamically adjust their construction parameters according to the prevalence rates and thus can be a better alternative than using a fixed pooling matrix.
Moreover, we exploit positive correlations between samples within a group. We prove that further cost reduction can be achieved using the Dorfman two-stage method when samples within a group are positively correlated. Finally, we propose a hierarchical agglomerative algorithm for pooled testing with a social graph, where an edge in the social graph connects frequent social contacts between two persons. This algorithm reduces notable cost reduction (roughly 20%–35%) compared to random pooling when the Dorfman two-stage algorithm is applied.
[1] Z. Gu, Y. Wang, Q.-S. Hua, and F. C. M. Lau, Rendezvous in Distributed Systems: Theory, Algorithms and Applications. Springer, 2017.
[2] L. Chen, Y. Li, and A. V. Vasilakos, “Oblivious neighbor discovery for wireless devices with directional antennas,” in Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2016, pp. 1–9.
[3] S. A. Pambudi, W. Wang, and C. Wang, “Fast rendezvous for spectrum-agile IoT devices with limited channel hopping capability,” in Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2018, pp. 1385–1393.
[4] Z. Zhang, B. Yang, M. Liu, Z Li, and X. Guo, “A quaternary-encoding-based channel hopping algorithm for blind rendezvous in distributed IoTs,” IEEE Trans. Commun., vol. 67, no. 10, pp. 7316–7330, Oct. 2019.
[5] K. Bian and J.-M. Park, “Maximizing rendezvous diversity in rendezvous protocols for decentralized cognitive radio networks,” IEEE Trans. Mobile Comput., vol. 12, no. 7, pp. 1294–1307, 2013.
[6] Z. Gu, Q.-S. Hua, Y. Wang, and F. C. M. Lau, “Nearly optimal asynchronous blind rendezvous algorithm for cognitive radio networks,” in Proc. IEEE Int. Conf. Sens., Commun. Netw. (SECON), Jun. 2013, pp. 371–379.
[7] F. Hou, L. X. Cai, X. Shen, and J. Huang, “Asynchronous multichannel MAC design with difference-set-based hopping sequences,” IEEE Trans. Veh. Technol., vol. 60, no. 4, pp. 1728–1739, May 2011.
[8] J. Shin, D. Yang, and C. Kim, “A channel rendezvous scheme for cognitive radio networks,” IEEE Commun. Lett., vol. 14, no. 10, pp. 954–956, 2010.
[9] Z. Lin, H. Liu, X. Chu, and Y.-W. Leung, “Jump-stay based channel-hopping algorithm with guaranteed rendezvous for cognitive radio networks,” in Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2011, pp. 2444–2452.
[10] G. Y. Chang, J. F. Huang, and Y. S. Wang, “Matrix-based channel hopping algorithms for cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 14, no. 5, pp. 2755–2768, May 2015.
[11] B. Yang, M. Zheng, and W. Liang, “A time-efficient rendezvous algorithm with a full rendezvous degree for heterogeneous cognitive radio networks,” in IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2016, pp. 1–9.
[12] J. Singer, “A theorem in finite projective geometry and some applications to number theory,” Trans. Amer. Soc., vol. 43, no. 3, pp. 377–385, 1938.
[13] P. V. Kumar, “On the existence of square dot-matrix patterns having a specific three-valued periodic-correlation function,” IEEE Trans. Inf. Theory, vo. 34, no. 22, pp. 271–277, 1988.
[14] G.-Y. Chang and J.-F. Huang, “A fast rendezvous channel-hopping algorithm for cognitive radio networks,” IEEE Commun. Lett., vol. 17, no. 7, pp. 1475–1478, 2013.
[15] Y. Fu et al., “How local information improves rendezvous in cognitive radio networks,” in Proc. IEEE Int. Conf. Sens., Commun., Netw. (SECON), Jun. 2018, pp. 1–9.
[16] C.-S. Chang, J.-P. Sheu, and Y.-J. Lin, “On the theoretical gap of channel hopping sequences with maximum rendezvous diversity in the multichannel rendezvous problem,” IEEE/ACM Trans. Netw., vol. 29, no.4, pp. 1620–1633, Aug. 2021.
[17] Y.-J. Lin and C.-S. Chang, “PPoL: A periodic channel hopping sequence with nearly full rendezvous diversity,” in Proc. 30th Wireless Opt. Commun. Conf. (WOCC), 2021, pp 199–203.
[18] “Coronavirus disease (COVID-19) outbreak,” 2020. [Online]. Available: https://www.who.int/emergencies/diseases/novel-coronavirus-2019
[19] H. Nishiura et al., “Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19),” Int. J. Infect. Dis., vol. 94, 2020, Art. no. 154.
[20] Y.-C. Chen, P.-E. Lu, C.-S. Chang, and T.-H. Liu, “A time-dependent SIR model for COVID-19 with undetectable infected persons,” IEEE Trans. Netw. Sci. Eng., vol 7, no. 4, pp. 3279–3294, Oct.–Dec. 2020.
[21] “Pooled sample testing and screening testing for COVID-19,” 2020. [Online]. Available: https://www.fda.gov/medical-devices/coronavirus-covid-19-and-medical-devices/pooled-sample-testing-and-screening-testing-covid-19
[22] “Interim guidance for use of pooling procedures in SARS-CoV-2 diagnostic, screening, and surveillance testing,” 2020. [Online]. Available: https://www.cdc.gov/coronavirus/2019-ncov/lab/pooling-procedures.html
[23] R. Dorfman, “The detection of defective members of large populations,” Ann. Math. Statist., vol. 14, no. 4, pp. 436–440, 1943.
[24] N. Sinnott-Armstrong, D. Klein, and B. Hickey, “Evaluation of group testing for SARS-CoV-2 RNA,” medRxiv, 2020.
[25] N. Shental et al., “Efficient high-throughput SARS-CoV-2 testing to detect asymptomatic carriers, ” Sci. Adv., vol. 6, no. 37, 2020, Art. no. eabc5961.
[26] S. Ghosh et al., “Tapestry: A single-round smart pooling technique for COVID-19 testing,” medRxiv, 2020.
[27] S. Ghosh et al., “A compressed sensing approach to group-testing for COVID-19 detection,” 2020, arXiv:2005.07895.
[28] J. Yi, R. Mudumbai, and W. Xu, “Low-cost and high-throughput testing of COVID-19 viruses and antibodies via compressed sensing: System concepts and computational experiments,” 2020, arXiv:2004.05759.
[29] A. Heidarzadeh and K. Narayanan, “Two-stage adaptive pooling with RT-qPCR for COVID-19 screening,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), 2021.
[30] M. Aldridge, O. Johnson, and J. Scarlett, “Group testing: An information theory perspective,” Found. Trends Commun. Inf. Theory, vol. 15, no. 3–4, pp. 196–392, 2019.
[31] Y.-J. Lin, C.-H. Yu, T.-H. Liu, C.-S. Chang, and W.-T. Chen, “Constructions and Comparisons of Pooling Matrices for Pooled Testing of COVID-19,” IEEE Trans. Netw. Sci. Eng., vol. 9, no. 2, pp. 467–480, Mar.–Apr. 2022.
[32] S. D. Lendle, M. G. Hudgens, and B. F. Qaqish, “Group testing for case identification with correlated responses,” Biometrics, vol. 68, pp. 532–540, 2012.
[33] A. Deckert, T. Bärnighausen, and N. N. Kyei, “Simulation of pooled-sample analysis strategies for COVID-19 mass testing,” Bull. World Health Org., vol. 98, no. 9, pp. 590–598, 2020.
[34] M. Newman, Networks: An Introduction. London, U.K.: Oxford Univ. Press, 2010.
[35] Y.-J. Lin, C.-H. Yu, T.-H. Liu, C.-S. Chang, and W.-T. Chen, “Positively correlated samples save pooled testing costs,” IEEE Trans. Netw. Sci. Eng., vol. 8, no. 3, pp. 2170–2182, Jul.–Sep. 2021.
[36] C.-F. Shih, T.-Y. Wu, and W. Liao, “DH-MAC: A dynamic channel hopping MAC protocol for cognitive radio networks,” in Proc. IEEE Int. Conf. Commun. (ICC), May 2010, pp. 1–5.
[37] J. Li and Jiang Xie, “Practical fast multiple radio blind rendezvous schemes in ad-hoc cognitive radio networks,” in Proc. Resilience Week (RWS), Aug. 2015, pp. 1–6.
[38] R. N. Yadav, R. Misra, “Periodic channel-hopping sequence for rendezvous in cognitive radio networks,” in Proc. Int. Conf. Adv. Comput., Commun. Informat. (ICACCI), Aug. 2015, pp. 1787–1792.
[39] L. Yu, H. Liu, Y.-W. Leung, X. Chu, and Z. Lin, “Channel-hopping based on available channel set for rendezvous of cognitive radios,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2014, pp. 1573–1579.
[40] E. J. Anderson and R. Weber, “The rendezvous problem on discrete locations,” J. Appl. Probab., vol. 27, no. 4, pp. 839–851, Dec. 1990.
[41] A. Dessmark, P. Fraigniaud, D. R. Kowalski, A. Pelc, “Deterministic rendezvous in graphs,” Algorithmica, vol. 46, no. 1, pp. 69–96, Sep. 2006.
[42] C.-S. Chang, C.-Y. Chen, D.-S. Lee, and W. Liao, “Efficient encoding of user IDs for nearly optimal expected time-to-rendezvous in heterogeneous cognitive radio networks,” IEEE/ACM Trans. Netw., vol. 25, no. 6, pp. 3323–3337, Dec. 2017.
[43] N. C. Theis, R. W. Thomas, and L. A. DaSilva, “Rendezvous for cognitive radios,”
IEEE Trans. Mobile Comput., vol. 10, no. 2, pp. 216–227, Feb. 2011.
[44] Z. Gu, Q.-S. Hua, and W. Dai, “Fully distributed algorithm for blind rendezvous in cognitive radio networks,” in Proc. ACM MobiHoc, Aug 2014, pp. 155–164.
[45] L. Chen, K. Bian, L. Chen, C. Liu, J. M. J. Park, and X. Li, “A group-theoretic framework for rendezvous in heterogeneous cognitive radio networks,” in Proc. ACM MobiHoc, Aug. 2014, pp. 165–174.
[46] L. Chen, S. Shi, K. Bian, and Y. Ji, “Optimizing average-maximum TTR trade-off for cognitive radio rendezvous,” in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2015, pp. 7707-7712.
[47] S. Chen, A. Russell, A. Samanta, and R. Sundaram, “Deterministic blind rendezvous in cognitive radio networks.” in Proc. IEEE Int. Conf. Distrib. Comput. Syst. (ICDCS), Jun. 2014, pp. 358–367.
[48] S. Alpern and S. Gal. The Theory of Search Games and Rendezvous. Dordrecht, The Netherlands: Kluwer, 2003.
[49] C.-S. Chang, W. Liao, and C.-M. Lien, “On the multichannel rendezvous problem: Fundamental limits, optimal hopping sequences, and bounded time-to-rendezvous,” Math. Oper. Res., vol. 40, no. 1, pp. 1–23, Feb. 2015.
[50] D. Yang, J. Shin, and C. Kim, “Deterministic rendezvous scheme in multichannel access networks,” Electron. Lett., vol. 46, no. 20, pp. 1402–1404, 2010.
[51] C.-S. Chang, W. Liao, and T.-Y. Wu, “Tight lower bounds for channel hopping schemes in cognitive radio networks,” IEEE/ACM Trans. Netw., vol. 24, no. 4, pp. 2343–2356, Aug. 2016.
[52] Y. Zhang, Y.-H. Lo, and W. S. Wong, “On channel hopping sequences with full rendezvous diversity for cognitive radio networks,” IEEE Wireless Commun. Lett., vol. 7, no. 4, pp. 574–577, Aug. 2018.
[53] Y. R. Kondareddy and P. Agrawal, “Synchronized MAC protocol for multi-hop cognitive radio networks,” in Proc. IEEE Int. Conf. Commun. (ICC), May 2008, pp. 3198–3202.
[54] K. Bian, J.-M. Park, and R. Chane, “A quorum-based framework for establishing control channels in dynamic spectrum access networks,” in Proc. Int. Conf. Mobile Comput. Netw. (MobiCom), Sep. 2009, pp. 25–36.
[55] P. Bahl, R. Chandra, J. Dunagan, “SSCH: slotted seeded channel hopping for capacity improvement in IEEE 802.11 ad-hoc wireless networks,” in Proc. Int. Conf. Mobile Comput. Netw. (MobiCom), Sep. 2004, pp. 216–230.
[56] L. DaSilva and I. Guerreiro, “Sequence based rendezvous for dynamic spectrum access,” in Proc. IEEE Symp. Frontiers Dyn. Spectr. Access Netw. (DySPAN), Oct. 2008, pp. 1–7.
[57] Z, Lin, H. Liu, X. Chu, and Y.-W. Leung, “Enhanced jump-stay rendezvous algorithm for cognitive radio networks,” IEEE Commun. Lett., vol. 17, no. 9, pp. 1742–1745, Sep. 2013.
[58] G.-Y. Chang, W.-H. Teng, H.-Y. Chen, and J.-P. Sheu, “Novel channel-hopping schemes for cognitive radio networks,” IEEE Trans. Mobile Comput., vol. 13, pp. 407–421, Feb. 2014.
[59] I.-H. Chuang, H.-Y. Wu, and Y.-H. Kuo, “A fast blind rendezvous method by alternate hop-and-wait channel hopping in cognitive radio networks,” IEEE Trans. Mobile Comput., vol. 13, no. 10, pp. 2171–2184, Oct. 2014.
[60] C.-S. Chang, Y.-C. Chang, and J.-P. Sheu, “A quasi-random algorithms for anonymous rendezvous in heterogeneous cognitive radio networks,” 2019, arXiv:1902.06933.
[61] Z. Gu, H. Pu, Q.-S. Hua, and F. C. M. Lau, “Improved rendezvous algorithms for heterogeneous cognitive radio networks,” in Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2015, pp. 154–162.
[62] Y.-C. Chang, C.-S. Chang, and J.-P. Sheu, “An enhanced fast multi-radio rendezvous algorithm in heterogeneous cognitive radio networks,” IEEE Trans. Cognit. Commun. Netw., vol. 4, no. 4, pp. 847–859, Dec. 2018.
[63] K. Wu, F. Han, F. Han, and D. Kong, “Rendezvous sequence construction in cognitive radio ad-hoc networks based on difference sets,” in Proc. IEEE Int. Symp. Pers., Indoor, Mobile Radio Commun. (PIMRC), Sep. 2013, pp. 1840–1845.
[64] X. J. Tan, C. Zhou, and J. Chen, “Symmetric channel hopping for blind rendezvous in cognitive radio networks based on union of disjoint difference sets,” IEEE Trans. Veh. Technol., vol. 66, no. 11, pp. 10233-10248, Nov. 2017.
[65] J. E. H. Elliott and A. T. Butson, “Relative difference sets,” Illinois J. Math., vol. 10, no. 3, pp. 517–531, Sep. 1966.
[66] W. S. Luk, and T. T. Wong, “Two new quorum based algorithms for distributed mutual exclusion,” in Proc. Int. Conf. Distrib. Comput. Syst. (ICDCS), May 1997, pp 100–106.
[67] R. C. Baker, G. Harman, and J. Pintz, “The difference between consecutive primes, II, ” in Proc. London Math. Soc., pp. 532–562, 2001.
[68] L. Euler, “Recherches sur une nouvelle espece de quarres magiques,” in Verhandelingen uitgegeven door het zeeuwsch Genootschap der Wetenschappen te Vlissingen, vol. 9, Middelburg, The Netherlands: Pieter Gillissen, 1782, pp. 85–239.
[69] C.-S. Chang, D.-S. Lee, and C. Wang, “Asynchronous grant-free uplink transmissions in multichannel wireless networks with heterogeneous QoS guarantees,” IEEE/ACM Trans. Netw., vol. 27, no. 4, pp. 1584–1597, Aug. 2019.
[70] S. Lohse et al., “Pooling of samples for testing for SARS-CoV-2 in asymptomatic people,” Lancet Infect. Dis., vol. 20, no. 11, pp. 1231–1232, 2020.
[71] B. Abdalhamid, C. R. Bilder, E. L. McCutchen, S. H. Hinrichs, S. A. Koepsell, and P. C. Iwen, “Assessment of specimen pooling to conserve SARS CoV-2 testing resources,” Amer. J. Clin. Pathol., vol. 153, no. 6, pp. 715–718, 2020.
[72] I. Yelin et al., Evaluation of COVID-19 RT-qPCR test in multi-sample pools,” Clin. Infect. Dis., vol. 71, no. 16, pp. 2073–2078, 2020.
[73] C. Gollier and O. Gossner, “Group testing against COVID-19,” Covid Econo., vol. 2, 2020.
[74] I. S. Reed and G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Ind. Appl. Math., vol. 8, no. 2, pp. 300–304, 1960.
[75] D. Hong, R. Dey, X. Lin, B. Cleary, and E. Dobriban, “HYPER: Group testing via hypergraph factorization applied to COVID-19,” medRxiv, 2021.
[76] M. Täufer, “Rapid, large-scale, and effective detection of COVID-19 via nonadaptive testing,” J. Theor. Biol., vol. 506, 2020, Art. no. 110450.
[77] W. Kautz and R. Singleton, “Nonrandom binary superimposed codes,” IEEE Trans. Inf. Theory, vol. 10, no. 4, pp. 363–377, Oct. 1964.
[78] “List of countries implementing pool testing strategy against COVID-19,” 2020. [Online]. Available: https://en.wikipedia.org/wiki/List_of_countries_ implementing_pool_testing_strategy_against_COVID-19
[79] L. Mutesa et al., “A pooled testing strategy for identifying SARS-CoV-2 at low prevalence,” Nature, vol. 589, pp. 276–280, 2021.
[80] C.-S. Chang, C.-Y. Hsu, J. Cheng, and D.-S. Lee, “A general probabilistic framework for detecting community structure in networks,” in Proc. IEEE Int. Conf. Comput. Commun. (INFOCOM), Apr. 2011, pp. 730–738.
[81] C.-S. Chang, C.-J. Chang, W.-T. Hsieh, D.-S. Lee, L.-H. Liou, and W. Liao, “Relative centrality and local community detection,” Netw. Sci., vol. 3, no. 4, pp. 445–479, 2015.
[82] C.-S. Chang, D.-S. Lee, L.-H. Liou, S.-M. Lu, and M.-H. Wu, “A probabilistic framework for structural analysis and community detection in directed networks,” IEEE/ACM Trans. Netw., vol. 26, no. 1, pp. 31–46, Feb. 2017.
[83] R. Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling. New York, NY, USA: Springer, 2013.
[84] W. W. Zachary, “An information flow model for conflict and fission in small groups,” J. Anthropol. Res., vol. 33, no. 4, pp. 452–473, 1977.
[85] M. Hung and W. H. Swallow, “Robustness of group testing in the estimation of proportions,” Biometrics, vol. 55, no. 1, pp. 231–237, 1999.
[86] D. J. Watts and S. H. Strogatz, “Collective dynamics of｀small-world＇networks,” Nature, vol. 393, pp. 440–442, 1998.
[87] H. Yin, A. R. Benson, J. Leskovec, and D. F. Gleich, “Local higher-order graph clustering,” in Proc. 23rd ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2017, pp. 555–564.
[88] J. Leskovec, J. Kleinberg, and C. Faloutsos, “Graph evolution: Densification and shrinking diameters,” ACM Trans. Knowl. Discov. Data, vol. 1, no. 1, p. 2, 2007.
[89] L. A. Adamic and N. Glance, “The political blogosphere and the 2004 US election: Divided they blog,” in Proc. 3rd Int. Workshop Link Discov., 2005, pp. 36–43.
[90] J. Leskovec and J. J. Mcauley, “Learning to discover social circles in ego networks,” in Proc. Adv. Neural Inf. Process. Syst., 2012, pp. 539–547.
[91] P.-E. Lu and C.-S. Chang, “Explainable, stable, and scalable graph convolutional networks for learning graph representation,” 2020, arXiv:2009.10367.
[92] D. Kempe, J. Kleinberg, and É. Tardos, “Maximizing the spread of influence through a social network,” in Proc. 9th ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2003, pp. 137–146.
[93] J. D. Esary, F. Proschan, and D. W. Walkup, “Association of random variables, with applications,” Ann. Math. Statist., vol. 38, no. 5, pp. 1466–1474, 1967.
[94] P. Nikolopoulos, S. R. Srinivasavaradhan, T. Guo, C. Fragouli, and S. Diggavi,“Group testing for connected communities,” in Proc. Int. Conf. Artif. Intell. Statist., 2021, pp. 2341–2349.
[95] P. Nikolopoulos, S. R. Srinivasavaradhan, T. Guo, C. Fragouli, and S. Diggavi,“Group testing for overlapping communities,” 2021, arXiv:2012.02804.