{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T02:04:52Z","timestamp":1725674692967},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642293436"},{"type":"electronic","value":"9783642293443"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-29344-3_46","type":"book-chapter","created":{"date-parts":[[2012,4,10]],"date-time":"2012-04-10T10:19:29Z","timestamp":1334053169000},"page":"542-555","source":"Crossref","is-referenced-by-count":0,"title":["Random Walks and Bisections in Random Circulant Graphs"],"prefix":"10.1007","author":[{"given":"Bernard","family":"Mans","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Igor E.","family":"Shparlinski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"46_CR1","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1017\/S0963548311000125","volume":"20","author":"N. Alon","year":"2011","unstructured":"Alon, N., Avin, C., Kouck, M., Kozma, G., Lotker, Z., Tuttle, M.R.: Many random walks are faster than one. Combin., Prob. and Comp.\u00a020, 481\u2013502 (2011)","journal-title":"Combin., Prob. and Comp."},{"key":"46_CR2","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1515\/gcc.2010.004","volume":"2","author":"G. Amir","year":"2010","unstructured":"Amir, G., Gurel-Gurevich, O.: The diameter of a random Cayley graph of \u2124 q . Groups Complex. Crypto.\u00a02, 59\u201365 (2010)","journal-title":"Groups Complex. Crypto."},{"key":"46_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/3-540-48686-0_36","volume-title":"Computing and Combinatorics","author":"J.-Y. Cai","year":"1999","unstructured":"Cai, J.-Y., Havas, G., Mans, B., Nerurkar, A., Seifert, J.-P., Shparlinski, I.E.: On Routing in Circulant Graphs. In: Asano, T., Imai, H., Lee, D.T., Nakano, S.-i., Tokuyama, T. (eds.) COCOON 1999. LNCS, vol.\u00a01627, pp. 360\u2013369. Springer, Heidelberg (1999)"},{"key":"46_CR4","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/BF01192695","volume":"29","author":"Y.O. Hamidoune","year":"1996","unstructured":"Hamidoune, Y.O., Serra, O.: On small cuts separating an Abelian Cayley graph into two equal parts. Math. Systems Theory\u00a029, 407\u2013409 (1996)","journal-title":"Math. Systems Theory"},{"key":"46_CR5","volume-title":"An Introduction to the theory of numbers","author":"G.H. Hardy","year":"1979","unstructured":"Hardy, G.H., Wright, E.M.: An Introduction to the theory of numbers, 5th edn. The Clarendon Press, Oxford University Press, New York (1979)","edition":"5"},{"key":"46_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/inco.1996.2618","volume":"133","author":"J. Hromkovi\u010d","year":"1997","unstructured":"Hromkovi\u010d, J., Klasing, R., Unger, W., Wagener, H.: Optimal algorithms for broadcast and gossip in the edge-disjoint path modes. Information and Computation\u00a0133, 1\u201333 (1997)","journal-title":"Information and Computation"},{"key":"46_CR7","volume-title":"Analytic number theory","author":"H. Iwaniec","year":"2004","unstructured":"Iwaniec, H., Kowalski, E.: Analytic number theory. Amer. Math. Soc., Providence (2004)"},{"key":"46_CR8","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/S0166-218X(97)00112-1","volume":"83","author":"R. Klasing","year":"1998","unstructured":"Klasing, R.: The relationship between the gossip complexity in the vertex-disjoint paths mode and the vertex bisection width. Discr. Appl. Math.\u00a083, 229\u2013246 (1998)","journal-title":"Discr. Appl. Math."},{"key":"46_CR9","first-page":"105","volume":"30","author":"M. Laczkovich","year":"1995","unstructured":"Laczkovich, M.: Discrepancy estimates for sets with small boundary. Studia Sci. Math. Hungar.\u00a030, 105\u2013109 (1995)","journal-title":"Studia Sci. Math. Hungar."},{"key":"46_CR10","doi-asserted-by":"crossref","unstructured":"Leighton, F.T.: Introduction to parallel algorithms and architectures: Arrays, trees, hypercubes. M.\u00a0Kaufmann (1992)","DOI":"10.1016\/B978-1-4832-0772-8.50005-4"},{"key":"46_CR11","unstructured":"Lov\u00e1sz, L.: Random walks on graphs: A survey. Combinatorics, Paul Erd\u00f6s is Eighty, Bolyai Soc., 1\u201346 (1993)"},{"key":"46_CR12","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S0012-365X(01)00374-0","volume":"254","author":"B. Mans","year":"2002","unstructured":"Mans, B., Pappalardi, F., Shparlinski, I.: On the spectral \u00c1d\u00e1m property for circulant graphs. Discrete Math.\u00a0254, 309\u2013329 (2002)","journal-title":"Discrete Math."},{"key":"46_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/978-3-540-24698-5_61","volume-title":"LATIN 2004: Theoretical Informatics","author":"B. Mans","year":"2004","unstructured":"Mans, B., Shparlinski, I.E.: Bisecting and Gossiping in Circulant Graphs. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol.\u00a02976, pp. 589\u2013598. Springer, Heidelberg (2004)"},{"key":"46_CR14","unstructured":"Marklof, J., Strombergsson, A.: Diameters of random circulant graphs, Preprint (2011), http:\/\/arxiv.org\/abs\/1103.3152"},{"key":"46_CR15","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. In: Proc. 21st ACM-SIAM Symposium on Discrete Algorithms, pp. 1468\u20131480. ACM Press (2010)","DOI":"10.1137\/1.9781611973075.119"},{"key":"46_CR16","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations. In: Proc. 42nd ACM Symp. Theory of Comp., pp. 351\u2013358. ACM Press (2010)","DOI":"10.1145\/1806689.1806739"},{"key":"46_CR17","doi-asserted-by":"crossref","unstructured":"Muzychuk, M.: On \u00c1d\u00e1m\u2019s conjecture for circulant graphs. Discrete Math.\u00a0167\/168, 497\u2013510 (1997); erratum: ibid. 176, 285\u2013298 (1997)","DOI":"10.1016\/S0012-365X(96)00251-8"},{"key":"46_CR18","volume-title":"The LLL algorithm: Survey and applications","author":"P.Q. Nguyen","year":"2009","unstructured":"Nguyen, P.Q., Vall\u00e9e, B.: The LLL algorithm: Survey and applications. Springer, Heidelberg (2009)"},{"key":"46_CR19","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1137\/070705702","volume":"39","author":"P.Q. Nguyen","year":"2009","unstructured":"Nguyen, P.Q., Stehl\u00e9, D.: An LLL algorithm with quadratic complexity. SIAM J. Comput.\u00a039, 874\u2013903 (2009)","journal-title":"SIAM J. Comput."},{"key":"46_CR20","unstructured":"Pujol, X., Stehl\u00e9, D.: Solving the shortest lattice vector problem in time 22.465n \u2019, Cryptology ePrint Archive, Report 2009\/605 (2009), http:\/\/eprint.iacr.org\/2009\/605"},{"key":"46_CR21","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/BF01190941","volume":"144","author":"H. Niederreiter","year":"1975","unstructured":"Niederreiter, H., Wills, J.M.: Diskrepanz und Distanz von Massen bezuglich konvexer und Jordanscher Mengen. Math. Z.\u00a0144, 125\u2013134 (1975)","journal-title":"Math. Z."}],"container-title":["Lecture Notes in Computer Science","LATIN 2012: Theoretical Informatics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-29344-3_46.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,23]],"date-time":"2020-11-23T22:04:33Z","timestamp":1606169073000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-29344-3_46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642293436","9783642293443"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-29344-3_46","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}