Strong difference families over arbitrary graphs

2008 ◽  
Vol 16 (6) ◽  
pp. 443-461 ◽  
Author(s):  
Marco Buratti ◽  
Lucia Gionfriddo
Keyword(s):  
Difference Families ◽  
Strong Difference ◽  
Arbitrary Graphs

scholarly journals Strong difference families of special types

2020 ◽  
Vol 343 (4) ◽  
pp. 111776 ◽  
Author(s):  
Yanxun Chang ◽  
Simone Costa ◽  
Tao Feng ◽  
Xiaomiao Wang
Keyword(s):  
Difference Families ◽  
Strong Difference

Existence of strong difference families and constructions for eight new 2‐designs

2021 ◽  
Author(s):  
Xiaomiao Wang ◽  
Tao Feng ◽  
Shixin Wang
Keyword(s):  
Difference Families ◽  
Strong Difference

scholarly journals New 2-designs from strong difference families

2018 ◽  
Vol 50 ◽  
pp. 391-405 ◽  
Author(s):  
Simone Costa ◽  
Tao Feng ◽  
Xiaomiao Wang
Keyword(s):  
Difference Families ◽  
Strong Difference

New Classes of Optimal Variable-Weight Optical Orthogonal Codes Based on Cyclic Difference Families

2010 ◽  
Vol E93-A (11) ◽  
pp. 2232-2238 ◽  
Author(s):  
Dianhua WU ◽  
Pingzhi FAN ◽  
Xun WANG ◽  
Minquan CHENG
Keyword(s):  
Optical Orthogonal Codes ◽  
Difference Families ◽  
Orthogonal Codes ◽  
Variable Weight

scholarly journals Improving the Smoothed Complexity of FLIP for Max Cut Problems

2021 ◽  
Vol 17 (3) ◽  
pp. 1-38
Author(s):  
Ali Bibak ◽  
Charles Carlson ◽  
Karthekeyan Chandrasekaran
Keyword(s):  
General Framework ◽  
Edge Weight ◽  
Complete Graphs ◽  
Worst Case ◽  
Weight Density ◽  
Complete Problems ◽  
Substantial Progress ◽  
Run Time ◽  
Optimum Solution ◽  
Arbitrary Graphs

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .

Partitioned difference families versus zero-difference balanced functions

2019 ◽  
Vol 87 (11) ◽  
pp. 2461-2467 ◽  
Author(s):  
Marco Buratti ◽  
Dieter Jungnickel
Keyword(s):  
Difference Families

scholarly journals A criterion for residual 𝑝-finiteness of arbitrary graphs of finite 𝑝-groups

2019 ◽  
Vol 22 (5) ◽  
pp. 837-844
Author(s):  
Gareth Wilkes
Keyword(s):  
Fundamental Group ◽  
Infinite Graphs ◽  
Graphs Of Groups ◽  
Arbitrary Graphs

Abstract We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite. The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.

scholarly journals Succinct encoding of arbitrary graphs

2013 ◽  
Vol 513 ◽  
pp. 38-52 ◽  
Author(s):  
Arash Farzan ◽  
J. Ian Munro
Keyword(s):  
Arbitrary Graphs
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