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FPTAS for #BIS with Degree Bounds on One Side

Jingcheng Liu, Pinyan Lu
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
There is no restriction for the degrees on the other side, which do not even have to be bounded by a constant. Previously, FPTAS was only known for instances with a maximum degree of 5 for both sides.  ...  We design a very simple deterministic fully polynomial-time approximation scheme (FPTAS) for #BIS when the maximum degree for one side is no larger than 5.  ...  Jingcheng Liu (UC Berkeley) O #BIS 8 / 20 An FPTAS for #BIS with maximum degree bounds on one side, namely∆ ≤ 5.  ... 
doi:10.1145/2746539.2746598 dblp:conf/stoc/LiuL15 fatcat:37e7b5i2qbgidjxcyqcvhlrgbq

Counting Independent Sets and Colorings on Random Regular Bipartite Graphs

Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
In the weighted case, for all sufficiently large integers ∆ and weight parameters λ = Ω 1 ∆ , we also obtain an FPTAS on almost every ∆-regular bipartite graph.  ...  (q), there is an FPTAS to count the number of q-colorings on almost every ∆-regular bipartite graph.  ...  #BIS-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region. J. Comput. Syst.  ... 
doi:10.4230/lipics.approx-random.2019.34 dblp:conf/approx/LiaoLLM19 fatcat:ip6tpov4sjbb3a5k54pxpvzlbm

Counting independent sets and colorings on random regular bipartite graphs [article]

Chao Liao, Jiabao Lin, Pinyan Lu, Zhenyu Mao
2019 arXiv   pre-print
In the weighted case, for all sufficiently large integers Δ and weight parameters λ=Ω̃(1/Δ), we also obtain an FPTAS on almost every Δ-regular bipartite graph.  ...  , there is an FPTAS to count the number of q-colorings on almost every Δ-regular bipartite graph.  ...  Surprisingly, Liu and Lu [LL15] designed an FPTAS for #BIS which only requires one side of the vertex partition to be of maximum degree ∆ ≤ 5.  ... 
arXiv:1903.07531v1 fatcat:enbkxxpa2vdz7p754dwz235zjq

Algorithms for #BIS-hard problems on expander graphs [chapter]

Matthew Jenssen, Peter Keevash, Will Perkins
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
We give an FPTAS and an efficient sampling algorithm for the high-fugacity hard-core model on bounded-degree bipartite expander graphs and the low-temperature ferromagnetic Potts model on bounded-degree  ...  The computational complexity of the approximate counting and sampling problems for the hard-core model is well understood for bounded-degree graphs.  ...  Galanis,Štefankovič, Vigoda, and Yang [13] showed that approximating the ferromagnetic Potts model partition function for q ≥ 3 is #BIS-hard on graphs of maximum degree ∆ when β > β o (q, ∆), the order  ... 
doi:10.1137/1.9781611975482.135 dblp:conf/soda/JenssenKP19 fatcat:nvvcwyd7d5hj3ashc27iphf4aa

Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems

Heng Guo, Pinyan Lu, Marc Herbstritt
2016 International Workshop on Approximation Algorithms for Combinatorial Optimization  
For graphs with degree bound βγ−1 , regardless of the field (even inconsistent fields are allowed), correlation decay always holds and FPTAS exists.  ...  The uniqueness condition implies spatial mixing, and an FPTAS for the partition function exists based on spatial mixing.  ...  Acknowledgement We thank Liang Li, Jingcheng Liu, and Chihao Zhang for some stimulating discussion. In particular, the example of the 5-7 tree in Section 5 is an outcome from such discussion.  ... 
doi:10.4230/lipics.approx-random.2016.31 dblp:conf/approx/GuoL16 fatcat:op2stxhfdffmdmptwdxru4ycce

Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems

Heng Guo, Pinyan Lu
2018 ACM Transactions on Computation Theory  
For graphs with degree bound βγ−1 , regardless of the field (even inconsistent fields are allowed), correlation decay always holds and FPTAS exists.  ...  The uniqueness condition implies spatial mixing, and an FPTAS for the partition function exists based on spatial mixing.  ...  Acknowledgement We thank Liang Li, Jingcheng Liu, and Chihao Zhang for some stimulating discussion. In particular, the example of the 5-7 tree in Section 5 is an outcome from such discussion.  ... 
doi:10.1145/3265025 fatcat:qb4wolm3pbfvbbatzw4tt3c4im

Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems [article]

Heng Guo, Pinyan Lu
2018 arXiv   pre-print
We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes.  ...  Our technique is based on the correlation decay framework. The main technical contribution is a new potential function, with which we establish a new kind of spatial mixing.  ...  We also thank anonymous referees for their meticulous check over the draft version.  ... 
arXiv:1511.00493v3 fatcat:zpaumhkfsjb3pfmz2e7er3adcy

FPTAS for Counting Monotone CNF [chapter]

Jingcheng Liu, Pinyan Lu
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
with maximum degree 4 .  ...  In addition, we study the hypergraph matching problem, which arises naturally towards a complete classification of bounded degree Boolean #CSP problems, and show an FPTAS for counting 3D matchings of hypergraphs  ...  For counting matchings, an FPRAS based on Markov Chain Monte Carlo (MCMC) is known for any graph [14] , and deterministic FPTAS is only known for graphs with bounded degree [2] .  ... 
doi:10.1137/1.9781611973730.101 dblp:conf/soda/LiuL15 fatcat:fzav2plqdffshiy2e33iau3qna

Algorithms for #BIS-Hard Problems on Expander Graphs

Matthew Jenssen, Peter Keevash, Will Perkins
2020 SIAM journal on computing (Print)  
Similarly, for the hard-core model on a bipartite expander graph with symmetry between the sides of the bipartition, one could follow the suggestion of [21] and start the Glauber dynamics in either the  ...  The computational complexity of the approximate counting and sampling problems for the hard-core model is well understood for bounded-degree graphs.  ... 
doi:10.1137/19m1286669 fatcat:cvn3rdusmncibiansjubwpz434

FPTAS for Counting Monotone CNF [article]

Jingcheng Liu, Pinyan Lu
2014 arXiv   pre-print
with maximum degree 4.  ...  In addition, we study the hypergraph matching problem, which arises naturally towards a complete classification of bounded degree Boolean #CSP problems, and show an FPTAS for counting 3D matchings of hypergraphs  ...  For counting matchings, an FPRAS based on Markov Chain Monte Carlo (MCMC) is known for any graph [14] , and deterministic FPTAS is only known for graphs with bounded degree [2] .  ... 
arXiv:1311.3728v2 fatcat:nvwgx5hqrrgfzpnsmltx3qrih4

The Complexity of Ferromagnetic Two-spin Systems with External Fields [article]

Jingcheng Liu, Pinyan Lu, Chihao Zhang
2014 arXiv   pre-print
Later, Goldberg and Jerrum proved that it is #BIS-hard for Ising model if we allow inconsistent external fields on different nodes.  ...  In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard,  ...  For instance, the problem of Anti-Ferro(β, γ, µ) on bipartite graphs with maximum degree ∆, is denoted shortly by Bi-Anti-Ferro ∆ (β, γ, µ).  ... 
arXiv:1402.4346v1 fatcat:iqlhq5ejkjby7caic23lnljrry

FPTAS for Hardcore and Ising Models on Hypergraphs [article]

Pinyan Lu, Kuan Yang, Chihao Zhang
2015 arXiv   pre-print
For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS where a slightly stronger condition holds.  ...  In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of  ...  FPTAS for #BIS with degree bounds on one side. In Proceedings of STOC (to appear), 2015. Jer95] Mark Jerrum. A very simple algorithm for estimating the number of k-colorings of a low-degree graph.  ... 
arXiv:1509.05494v1 fatcat:ldtpylqhhna23adm2kxlhonevi

A deterministic approximation algorithm for computing the permanent of a 0,1 matrix

David Gamarnik, Dmitriy Katz
2010 Journal of computer and system sciences (Print)  
The e n approximation factor can be improved to (k/(k − 1)) kn for the case of of matrices with row and column sums bounded by k, using the Schrijver's bound [Sch98] .  ...  A recent dramatic improvement was obtained by Jerrum, Sinclair and Vigoda [JSV04] , who constructed FPTAS for an arbitrary matrix with non-negative entries.  ...  Based on this observation we propose the following recursive algorithm for computing Perm(G).  ... 
doi:10.1016/j.jcss.2010.05.002 fatcat:esyuefgggfcipk364r6sae2qsu

Improved Approximation Algorithms for Item Pricing with Bounded Degree and Valuation

R. HAMANE, T. ITOH
2008 IEICE transactions on information and systems  
Based on the approximation algorithm for the bi- partite graph vertex pricing problem, Balcan and Blum de- rived a 1/4-approximation algorithm for the graph vertex pricing problem  ...  Bounded Pseudodegree Graphs 4.1 Bipartite Graphs with Bounded Pseudodegree For bipartite vertex pricing problems, Balcan and Blum [1, Theorem 1] showed a 1/2-approximation algorithm  ...  Itoh is a member of the Institute of Electronics, Information, and Communication Engineers of Japan, the Information Processing Society of Japan, the Association for Computing Machinery, and LA.  ... 
doi:10.1093/ietisy/e91-d.2.187 fatcat:2xxuyxwudbdtbfh3tsyxmxl4ja

The Complexity of Ferromagnetic Two-spin Systems with External Fields

Jingcheng Liu, Pinyan Lu, Chihao Zhang, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Later, Goldberg and Jerrum proved that it is #BIShard for Ising model if we allow inconsistent external fields on different nodes.  ...  In contrast to these two results, we prove that for any ferromagnetic two-state spin systems except the Ising model, there exists a threshold for external fields beyond which the problem is #BIS-hard,  ...  For instance, the problem of Anti-Ferro(β, γ, µ) on bipartite graphs with maximum degree ∆ is denoted shortly by Bi-Anti-Ferro ∆ (β, γ, µ).  ... 
doi:10.4230/lipics.approx-random.2014.843 dblp:conf/approx/LiuLZ14 fatcat:fwitvao7izfere56ytuag3qrli
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