Pub Date : 1999-09-01DOI: 10.1002/(SICI)1098-2418(199909)15:2%3C165::AID-RSA3%3E3.0.CO;2-B
Wansoo T. Rhee
{"title":"Some exact rates for the random weighted interval packing problem","authors":"Wansoo T. Rhee","doi":"10.1002/(SICI)1098-2418(199909)15:2%3C165::AID-RSA3%3E3.0.CO;2-B","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199909)15:2%3C165::AID-RSA3%3E3.0.CO;2-B","url":null,"abstract":"","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121427150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-09-01DOI: 10.1002/(SICI)1098-2418(199909)15:2%3C113::AID-RSA1%3E3.0.CO;2-S
D. Coppersmith, G. Sorkin
{"title":"Constructive bounds and exact expectations for the random assignment problem","authors":"D. Coppersmith, G. Sorkin","doi":"10.1002/(SICI)1098-2418(199909)15:2%3C113::AID-RSA1%3E3.0.CO;2-S","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199909)15:2%3C113::AID-RSA1%3E3.0.CO;2-S","url":null,"abstract":"","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126258087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-08-08DOI: 10.1002/1098-2418(200101)18:1%3C18::AID-RSA2%3E3.0.CO;2-M
A. Broder, M. Mitzenmacher
We provide several new results related to the concept of min-wise independence. Our main result is that any randomized sampling scheme for the relative intersection of sets based on testing equality of samples yields an equivalent min-wise independent family. Thus, in a certain sense, min-wise independent families are complete for this type of estimation. We also discuss the notion of robustness, a concept extending min-wise independence to allow more efficient use of it in practice. A surprising result arising from our consideration of robustness is that under a random permutation from a min-wise independent family, any element of a fixed set has an equal chance to get any rank in the image of the set, not only the minimum as required by definition.
{"title":"Completeness and robustness properties of min-wise independent permutations","authors":"A. Broder, M. Mitzenmacher","doi":"10.1002/1098-2418(200101)18:1%3C18::AID-RSA2%3E3.0.CO;2-M","DOIUrl":"https://doi.org/10.1002/1098-2418(200101)18:1%3C18::AID-RSA2%3E3.0.CO;2-M","url":null,"abstract":"We provide several new results related to the concept of min-wise independence. Our main result is that any randomized sampling scheme for the relative intersection of sets based on testing equality of samples yields an equivalent min-wise independent family. Thus, in a certain sense, min-wise independent families are complete for this type of estimation. We also discuss the notion of robustness, a concept extending min-wise independence to allow more efficient use of it in practice. A surprising result arising from our consideration of robustness is that under a random permutation from a min-wise independent family, any element of a fixed set has an equal chance to get any rank in the image of the set, not only the minimum as required by definition.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115444410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-08-08DOI: 10.1002/1098-2418(200103)18:2%3C116::AID-RSA1001%3E3.0.CO;2-2
A. Condon, R. Karp
The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups.
{"title":"Algorithms for graph partitioning on the planted partition model","authors":"A. Condon, R. Karp","doi":"10.1002/1098-2418(200103)18:2%3C116::AID-RSA1001%3E3.0.CO;2-2","DOIUrl":"https://doi.org/10.1002/1098-2418(200103)18:2%3C116::AID-RSA1001%3E3.0.CO;2-2","url":null,"abstract":"The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph l-partition problem is to partition the nodes of an undirected graph into l equal-sized groups so as to minimize the total number of edges that cross between groups.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"125 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129725166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-08-01DOI: 10.1002/(SICI)1098-2418(199908)15:1%3C43::AID-RSA3%3E3.0.CO;2-S
H. Garmo
The asymptotic distribution of the number of cycles of length l in a random r-regular graph is determined. The length of the cycles is defined as a function of the number of vertices n, thus l = l(n), and the length satisfies l(n) --> infinity as n --> in
{"title":"The asymptotic distribution of long cycles in random regular graphs","authors":"H. Garmo","doi":"10.1002/(SICI)1098-2418(199908)15:1%3C43::AID-RSA3%3E3.0.CO;2-S","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199908)15:1%3C43::AID-RSA3%3E3.0.CO;2-S","url":null,"abstract":"The asymptotic distribution of the number of cycles of length l in a random r-regular graph is determined. The length of the cycles is defined as a function of the number of vertices n, thus l = l(n), and the length satisfies l(n) --> infinity as n --> in","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125625742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-08-01DOI: 10.1002/(SICI)1098-2418(199908)15:1%3C93::AID-RSA4%3E3.0.CO;2-K
T. Bohman, Janko Gravner
A site in Z 2 becomes occupied with a certain probability as soon as it sees at least a threshold number of already occupied sites in its neighborhood. Such randomly growing sets have the following regularity property: a large fully occupied set exists within a xed distance (which does not increase with time) of every occupied point. This property suuces to prove convergence to an asymptotic shape.
{"title":"Random threshold growth dynamics","authors":"T. Bohman, Janko Gravner","doi":"10.1002/(SICI)1098-2418(199908)15:1%3C93::AID-RSA4%3E3.0.CO;2-K","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199908)15:1%3C93::AID-RSA4%3E3.0.CO;2-K","url":null,"abstract":"A site in Z 2 becomes occupied with a certain probability as soon as it sees at least a threshold number of already occupied sites in its neighborhood. Such randomly growing sets have the following regularity property: a large fully occupied set exists within a xed distance (which does not increase with time) of every occupied point. This property suuces to prove convergence to an asymptotic shape.","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122216742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1999-05-01DOI: 10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6
M. Talagrand
Ž . ABSTRACT: We prove through a precise exponential inequality that the logarithm of the N Ž size of the intersection of M random half spaces with the unit sphere of R resp., the 4N . discrete cube y1, 1 is, as Na`, a self averaging quantity. This provides justification for w Ž . x one of the first steps of a famous computation by E. Gardner J. Phys. A 21 1988 , 257]270 . Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199]213, 1999
{"title":"Self averaging and the space of interactions in neural networks","authors":"M. Talagrand","doi":"10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6","DOIUrl":"https://doi.org/10.1002/(SICI)1098-2418(199905)14:3%3C199::AID-RSA1%3E3.0.CO;2-6","url":null,"abstract":"Ž . ABSTRACT: We prove through a precise exponential inequality that the logarithm of the N Ž size of the intersection of M random half spaces with the unit sphere of R resp., the 4N . discrete cube y1, 1 is, as Na`, a self averaging quantity. This provides justification for w Ž . x one of the first steps of a famous computation by E. Gardner J. Phys. A 21 1988 , 257]270 . Q 1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 199]213, 1999","PeriodicalId":303496,"journal":{"name":"Random Struct. Algorithms","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124403441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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