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Documents authored by Xia, Yu

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Xia, Yu

Document
DOI: 10.4230/LIPIcs.ICALP.2016.64
Information Cascades on Arbitrary Topologies

Authors: Jun Wan, Yu Xia, Liang Li, and Thomas Moscibroda

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
In this paper, we study information cascades on graphs. In this setting, each node in the graph represents a person. One after another, each person has to take a decision based on a private signal as well as the decisions made by earlier neighboring nodes. Such information cascades commonly occur in practice and have been studied in complete graphs where everyone can overhear the decisions of every other player. It is known that information cascades can be fragile and based on very little information, and that they have a high likelihood of being wrong. Generalizing the problem to arbitrary graphs reveals interesting insights. In particular, we show that in a random graph G(n,q), for the right value of q, the number of nodes making a wrong decision is logarithmic in n. That is, in the limit for large n, the fraction of players that make a wrong decision tends to zero. This is intriguing because it contrasts to the two natural corner cases: empty graph (everyone decides independently based on his private signal) and complete graph (all decisions are heard by all nodes). In both of these cases a constant fraction of nodes make a wrong decision in expectation. Thus, our result shows that while both too little and too much information sharing causes nodes to take wrong decisions, for exactly the right amount of information sharing, asymptotically everyone can be right. We further show that this result in random graphs is asymptotically optimal for any topology, even if nodes follow a globally optimal algorithmic strategy. Based on the analysis of random graphs, we explore how topology impacts global performance and construct an optimal deterministic topology among layer graphs.
Cite as

Jun Wan, Yu Xia, Liang Li, and Thomas Moscibroda. Information Cascades on Arbitrary Topologies. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{wan_et_al:LIPIcs.ICALP.2016.64,
  author =	{Wan, Jun and Xia, Yu and Li, Liang and Moscibroda, Thomas},
  title =	{{Information Cascades on Arbitrary Topologies}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{64:1--64:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.64},
  URN =		{urn:nbn:de:0030-drops-63417},
  doi =		{10.4230/LIPIcs.ICALP.2016.64},
  annote =	{Keywords: Information Cascades, Herding Effect, Random Graphs}
}

Xia, Zhiyu

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.100
On the Degree of Boolean Functions as Polynomials over ℤ_m

Authors: Xiaoming Sun, Yuan Sun, Jiaheng Wang, Kewen Wu, Zhiyu Xia, and Yufan Zheng

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Polynomial representations of Boolean functions over various rings such as ℤ and ℤ_m have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of areas including communication complexity, circuit complexity, learning theory, coding theory and so on. For any integer m ≥ 2, each Boolean function has a unique multilinear polynomial representation over ring ℤ_m. The degree of such polynomial is called modulo-m degree, denoted as deg_m(⋅). In this paper, we investigate the lower bound of modulo-m degree of Boolean functions. When m = p^k (k ≥ 1) for some prime p, we give a tight lower bound deg_m(f) ≥ k(p-1) for any non-degenerate function f:{0,1}ⁿ → {0,1}, provided that n is sufficient large. When m contains two different prime factors p and q, we give a nearly optimal lower bound for any symmetric function f:{0,1}ⁿ → {0,1} that deg_m(f) ≥ n/{2+1/(p-1)+1/(q-1)}.
Cite as

Xiaoming Sun, Yuan Sun, Jiaheng Wang, Kewen Wu, Zhiyu Xia, and Yufan Zheng. On the Degree of Boolean Functions as Polynomials over ℤ_m. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 100:1-100:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sun_et_al:LIPIcs.ICALP.2020.100,
  author =	{Sun, Xiaoming and Sun, Yuan and Wang, Jiaheng and Wu, Kewen and Xia, Zhiyu and Zheng, Yufan},
  title =	{{On the Degree of Boolean Functions as Polynomials over \mathbb{Z}\underlinem}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{100:1--100:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.100},
  URN =		{urn:nbn:de:0030-drops-125070},
  doi =		{10.4230/LIPIcs.ICALP.2020.100},
  annote =	{Keywords: Boolean function, polynomial, modular degree, Ramsey theory}
}
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