4 Search Results for "Xia, Mingji"


Document
Sub-Exponential Time Lower Bounds for #VC and #Matching on 3-Regular Graphs

Authors: Ying Liu and Shiteng Chen

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
This article focuses on the sub-exponential time lower bounds for two canonical #P-hard problems: counting the vertex covers of a given graph (#VC) and counting the matchings of a given graph (#Matching), under the well-known counting exponential time hypothesis (#ETH). Interpolation is an essential method to build reductions in this article and in the literature. We use the idea of block interpolation to prove that both #VC and #Matching have no 2^{o(N)} time deterministic algorithm, even if the given graph with N vertices is a 3-regular graph. However, when it comes to proving the lower bounds for #VC and #Matching on planar graphs, both block interpolation and polynomial interpolation do not work. We prove that, for any integer N > 0, we can simulate N pairwise linearly independent unary functions by gadgets with only O(log N) size in the context of #VC and #Matching. Then we use log-size gadgets in the polynomial interpolation to prove that planar #VC and planar #Matching have no 2^{o(√{N/(log N)})} time deterministic algorithm. The lower bounds hold even if the given graph with N vertices is a 3-regular graph. Based on a stronger hypothesis, randomized exponential time hypothesis (rETH), we can avoid using interpolation. We prove that if rETH holds, both planar #VC and planar #Matching have no 2^{o(√N)} time randomized algorithm, even that the given graph with N vertices is a planar 3-regular graph. The 2^{Ω(√N)} time lower bounds are tight, since there exist 2^{O(√N)} time algorithms for planar #VC and planar #Matching. We also develop a fine-grained dichotomy for a class of counting problems, symmetric Holant*.

Cite as

Ying Liu and Shiteng Chen. Sub-Exponential Time Lower Bounds for #VC and #Matching on 3-Regular Graphs. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{liu_et_al:LIPIcs.STACS.2024.49,
  author =	{Liu, Ying and Chen, Shiteng},
  title =	{{Sub-Exponential Time Lower Bounds for #VC and #Matching on 3-Regular Graphs}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{49:1--49:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.49},
  URN =		{urn:nbn:de:0030-drops-197593},
  doi =		{10.4230/LIPIcs.STACS.2024.49},
  annote =	{Keywords: computational complexity, planar Holant, polynomial interpolation, rETH, sub-exponential, #ETH, #Matching, #VC}
}
Document
Two-State Spin Systems with Negative Interactions

Authors: Yumou Fei, Leslie Ann Goldberg, and Pinyan Lu

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a 2×2 symmetric matrix. Previous results on this problem were restricted either to the case where the matrix has non-negative entries, or to the case where the diagonal entries are equal, i.e. Ising models. In this paper, we study the generalization to arbitrary 2×2 interaction matrices with real entries. We show that in some regions of the parameter space, it’s #P-hard to even determine the sign of the partition function, while in other regions there are fully polynomial approximation schemes for the partition function. Our results reveal several new computational phase transitions.

Cite as

Yumou Fei, Leslie Ann Goldberg, and Pinyan Lu. Two-State Spin Systems with Negative Interactions. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{fei_et_al:LIPIcs.ITCS.2024.45,
  author =	{Fei, Yumou and Goldberg, Leslie Ann and Lu, Pinyan},
  title =	{{Two-State Spin Systems with Negative Interactions}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{45:1--45:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.45},
  URN =		{urn:nbn:de:0030-drops-195739},
  doi =		{10.4230/LIPIcs.ITCS.2024.45},
  annote =	{Keywords: Approximate Counting, Spin Systems, #P-Hardness, Randomized Algorithms}
}
Document
The Complexity of Weighted Boolean #CSP Modulo k

Authors: Heng Guo, Sangxia Huang, Pinyan Lu, and Mingji Xia

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)


Abstract
We prove a complexity dichotomy theorem for counting weighted Boolean CSP modulo k for any positive integer $k>1$. This generalizes a theorem by Faben for the unweighted setting. In the weighted setting, there are new interesting tractable problems. We first prove a dichotomy theorem for the finite field case where k is a prime. It turns out that the dichotomy theorem for the finite field is very similar to the one for the complex weighted Boolean #CSP, found by [Cai, Lu and Xia, STOC 2009]. Then we further extend the result to an arbitrary integer k.

Cite as

Heng Guo, Sangxia Huang, Pinyan Lu, and Mingji Xia. The Complexity of Weighted Boolean #CSP Modulo k. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 249-260, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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@InProceedings{guo_et_al:LIPIcs.STACS.2011.249,
  author =	{Guo, Heng and Huang, Sangxia and Lu, Pinyan and Xia, Mingji},
  title =	{{The Complexity of Weighted Boolean #CSP Modulo k}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{249--260},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.249},
  URN =		{urn:nbn:de:0030-drops-30158},
  doi =		{10.4230/LIPIcs.STACS.2011.249},
  annote =	{Keywords: #CSP, dichotomy theorem, counting problems, computational complexity}
}
Document
Extended Abstract
A Theory for Valiant's Matchcircuits (Extended Abstract)

Authors: Angsheng Li and Mingji Xia

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)


Abstract
The computational function of a matchgate is represented by its character matrix. In this article, we show that all nonsingular character matrices are closed under matrix inverse operation, so that for every $k$, the nonsingular character matrices of $k$-bit matchgates form a group, extending the recent work of Cai and Choudhary (2006) of the same result for the case of $k=2$, and that the single and the two-bit matchgates are universal for matchcircuits, answering a question of Valiant (2002).

Cite as

Angsheng Li and Mingji Xia. A Theory for Valiant's Matchcircuits (Extended Abstract). In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 491-502, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{li_et_al:LIPIcs.STACS.2008.1368,
  author =	{Li, Angsheng and Xia, Mingji},
  title =	{{A Theory for Valiant's Matchcircuits}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{491--502},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1368},
  URN =		{urn:nbn:de:0030-drops-13686},
  doi =		{10.4230/LIPIcs.STACS.2008.1368},
  annote =	{Keywords: Pfaffian, Matchgate, Matchcircuit}
}
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