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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.97

The SDP Value of Random 2CSPs

Authors: Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

We consider a very wide class of models for sparse random Boolean 2CSPs; equivalently, degree-2 optimization problems over {±1}ⁿ. For each model ℳ, we identify the "high-probability value" s^*_ℳ of the natural SDP relaxation (equivalently, the quantum value). That is, for all ε > 0 we show that the SDP optimum of a random n-variable instance is (when normalized by n) in the range (s^*_ℳ-ε, s^*_ℳ+ε) with high probability. Our class of models includes non-regular CSPs, and ones where the SDP relaxation value is strictly smaller than the spectral relaxation value.

Cite as

Amulya Musipatla, Ryan O'Donnell, Tselil Schramm, and Xinyu Wu. The SDP Value of Random 2CSPs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 97:1-97:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{musipatla_et_al:LIPIcs.ICALP.2022.97,
  author =	{Musipatla, Amulya and O'Donnell, Ryan and Schramm, Tselil and Wu, Xinyu},
  title =	{{The SDP Value of Random 2CSPs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{97:1--97:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.97},
  URN =		{urn:nbn:de:0030-drops-164381},
  doi =		{10.4230/LIPIcs.ICALP.2022.97},
  annote =	{Keywords: Random constraint satisfaction problems}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2022.91

Noisy Boolean Hidden Matching with Applications

Authors: Michael Kapralov, Amulya Musipatla, Jakab Tardos, David P. Woodruff, and Samson Zhou

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract

The Boolean Hidden Matching (BHM) problem, introduced in a seminal paper of Gavinsky et al. [STOC'07], has played an important role in lower bounds for graph problems in the streaming model (e.g., subgraph counting, maximum matching, MAX-CUT, Schatten p-norm approximation). The BHM problem typically leads to Ω(√n) space lower bounds for constant factor approximations, with the reductions generating graphs that consist of connected components of constant size. The related Boolean Hidden Hypermatching (BHH) problem provides Ω(n^{1-1/t}) lower bounds for 1+O(1/t) approximation, for integers t ≥ 2. The corresponding reductions produce graphs with connected components of diameter about t, and essentially show that long range exploration is hard in the streaming model with an adversarial order of updates. In this paper we introduce a natural variant of the BHM problem, called noisy BHM (and its natural noisy BHH variant), that we use to obtain stronger than Ω(√n) lower bounds for approximating a number of the aforementioned problems in graph streams when the input graphs consist only of components of diameter bounded by a fixed constant. We next introduce and study the graph classification problem, where the task is to test whether the input graph is isomorphic to a given graph. As a first step, we use the noisy BHM problem to show that the problem of classifying whether an underlying graph is isomorphic to a complete binary tree in insertion-only streams requires Ω(n) space, which seems challenging to show using either BHM or BHH.

Cite as

Michael Kapralov, Amulya Musipatla, Jakab Tardos, David P. Woodruff, and Samson Zhou. Noisy Boolean Hidden Matching with Applications. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 91:1-91:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kapralov_et_al:LIPIcs.ITCS.2022.91,
  author =	{Kapralov, Michael and Musipatla, Amulya and Tardos, Jakab and Woodruff, David P. and Zhou, Samson},
  title =	{{Noisy Boolean Hidden Matching with Applications}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{91:1--91:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.91},
  URN =		{urn:nbn:de:0030-drops-156876},
  doi =		{10.4230/LIPIcs.ITCS.2022.91},
  annote =	{Keywords: Boolean Hidden Matching, Lower Bounds, Communication Complexity, Streaming Algorithms}
}

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Documents authored by Musipatla, Amulya

The SDP Value of Random 2CSPs

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Noisy Boolean Hidden Matching with Applications

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