{"title":"动态业务平衡的扰动弹性集","authors":"Jin Sima, Chao Pan, Olgica Milenkovic","doi":"10.1007/s10623-025-01565-4","DOIUrl":null,"url":null,"abstract":"<p>A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in Pan et al. (in: 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, pp 2385–2390, 2022) for exchanging blocks of data chunks stored on distributed storage systems in an access- and load-balanced manner. More precisely, data chunks in the trades of interest are labeled by popularity ranks and the blocks are required to have both balanced overall popularity and stability properties with respect to swaps in chunk popularities. The original construction of such trades relied on computer search and paired balanced sets obtained through iterative combining of smaller sets that have provable stability guarantees. To reduce the substantial gap between the results of prior approaches and the known theoretical lower bound, we present new analytical upper and lower bounds on the minimal disbalance of blocks introduced by limited-magnitude popularity ranking swaps. Our constructive and near-optimal approach relies on pairs of graphs whose vertices are two balanced sets with edges/arcs that capture the balance and potential balance changes induced by limited-magnitude popularity swaps. In particular, we show that if we start with carefully selected balanced trades and limit the magnitude of rank swaps to one, the new upper and lower bound on the maximum block disbalance caused by a swap only differ by a factor of 1.07. We also extend these results for larger popularity swap magnitudes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"63 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Perturbation-resilient sets for dynamic service balancing\",\"authors\":\"Jin Sima, Chao Pan, Olgica Milenkovic\",\"doi\":\"10.1007/s10623-025-01565-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in Pan et al. (in: 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, pp 2385–2390, 2022) for exchanging blocks of data chunks stored on distributed storage systems in an access- and load-balanced manner. More precisely, data chunks in the trades of interest are labeled by popularity ranks and the blocks are required to have both balanced overall popularity and stability properties with respect to swaps in chunk popularities. The original construction of such trades relied on computer search and paired balanced sets obtained through iterative combining of smaller sets that have provable stability guarantees. To reduce the substantial gap between the results of prior approaches and the known theoretical lower bound, we present new analytical upper and lower bounds on the minimal disbalance of blocks introduced by limited-magnitude popularity ranking swaps. Our constructive and near-optimal approach relies on pairs of graphs whose vertices are two balanced sets with edges/arcs that capture the balance and potential balance changes induced by limited-magnitude popularity swaps. In particular, we show that if we start with carefully selected balanced trades and limit the magnitude of rank swaps to one, the new upper and lower bound on the maximum block disbalance caused by a swap only differ by a factor of 1.07. 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引用次数: 0
摘要
组合交易是在保持相关子集交叉约束的情况下可以交换的两组元素块。Pan等人(in: 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, pp 2385 - 2390,2022)提出了一类均衡和交换鲁棒最小交易,用于以访问和负载均衡的方式交换存储在分布式存储系统上的数据块。更准确地说,感兴趣的交易中的数据块通过流行度排名进行标记,并且要求块具有相对于块流行度交换的平衡的总体流行度和稳定性属性。这类交易的初始构造依赖于计算机搜索和由具有可证明稳定性保证的小集迭代组合得到的配对平衡集。为了减少先前方法的结果与已知理论下界之间的实质性差距,我们提出了由有限量级人气排名交换引入的最小块不平衡的新的解析上下界。我们的建设性和接近最优的方法依赖于图对,图对的顶点是两个带有边/弧的平衡集,这些边/弧捕获了由有限大小的人气交换引起的平衡和潜在的平衡变化。特别是,我们表明,如果我们从精心选择的平衡交易开始,并将等级互换的大小限制为1,则交换引起的最大区块不平衡的新上限和下限仅相差1.07因子。我们还将这些结果扩展到更大的人气交换幅度。
Perturbation-resilient sets for dynamic service balancing
A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in Pan et al. (in: 2022 IEEE International Symposium on Information Theory (ISIT), IEEE, pp 2385–2390, 2022) for exchanging blocks of data chunks stored on distributed storage systems in an access- and load-balanced manner. More precisely, data chunks in the trades of interest are labeled by popularity ranks and the blocks are required to have both balanced overall popularity and stability properties with respect to swaps in chunk popularities. The original construction of such trades relied on computer search and paired balanced sets obtained through iterative combining of smaller sets that have provable stability guarantees. To reduce the substantial gap between the results of prior approaches and the known theoretical lower bound, we present new analytical upper and lower bounds on the minimal disbalance of blocks introduced by limited-magnitude popularity ranking swaps. Our constructive and near-optimal approach relies on pairs of graphs whose vertices are two balanced sets with edges/arcs that capture the balance and potential balance changes induced by limited-magnitude popularity swaps. In particular, we show that if we start with carefully selected balanced trades and limit the magnitude of rank swaps to one, the new upper and lower bound on the maximum block disbalance caused by a swap only differ by a factor of 1.07. We also extend these results for larger popularity swap magnitudes.
期刊介绍:
Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines.
The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome.
The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas.
Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.