4 Search Results for "Jiang, He"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.103
The Support of Open Versus Closed Random Walks

Authors: Thomas Sauerwald, He Sun, and Danny Vagnozzi

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
A closed random walk of length 𝓁 on an undirected and connected graph G = (V,E) is a random walk that returns to the start vertex at step 𝓁, and its properties have been recently related to problems in different mathematical fields, e.g., geometry and combinatorics (Jiang et al., Annals of Mathematics '21) and spectral graph theory (McKenzie et al., STOC '21). For instance, in the context of analyzing the eigenvalue multiplicity of graph matrices, McKenzie et al. show that, with high probability, the support of a closed random walk of length 𝓁 ⩾ 1 is Ω(𝓁^{1/5}) on any bounded-degree graph, and leaves as an open problem whether a stronger bound of Ω(𝓁^{1/2}) holds for any regular graph. First, we show that the support of a closed random walk of length 𝓁 is at least Ω(𝓁^{1/2} / √{log n}) for any regular or bounded-degree graph on n vertices. Secondly, we prove for every 𝓁 ⩾ 1 the existence of a family of bounded-degree graphs, together with a start vertex such that the support is bounded by O(𝓁^{1/2}/√{log n}). Besides addressing the open problem of McKenzie et al., these two results also establish a subtle separation between closed random walks and open random walks, for which the support on any regular (or bounded-degree) graph is well-known to be Ω(𝓁^{1/2}) for all 𝓁 ⩾ 1. For irregular graphs, we prove that even if the start vertex is chosen uniformly, the support of a closed random walk may still be O(log 𝓁). This rules out a general polynomial lower bound in 𝓁 for all graphs. Finally, we apply our results on random walks to obtain new bounds on the multiplicity of the second largest eigenvalue of the adjacency matrices of graphs.
Cite as

Thomas Sauerwald, He Sun, and Danny Vagnozzi. The Support of Open Versus Closed Random Walks. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 103:1-103:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{sauerwald_et_al:LIPIcs.ICALP.2023.103,
  author =	{Sauerwald, Thomas and Sun, He and Vagnozzi, Danny},
  title =	{{The Support of Open Versus Closed Random Walks}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{103:1--103:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.103},
  URN =		{urn:nbn:de:0030-drops-181556},
  doi =		{10.4230/LIPIcs.ICALP.2023.103},
  annote =	{Keywords: support of random walks, eigenvalue multiplicity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.41
Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations

Authors: Chen Dan, Kristoffer Arnsfelt Hansen, He Jiang, Liwei Wang, and Yuchen Zhou

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
Low rank approximation of matrices is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns, and provides concise representations for the data. Research on low rank approximation usually focuses on real matrices. However, in many applications data are binary (categorical) rather than continuous. This leads to the problem of low rank approximation of binary matrices. Here we are given a d x n binary matrix A and a small integer k < d. The goal is to find two binary matrices U and V of sizes d x k and k x n respectively, so that the Frobenius norm of A - U V is minimized. There are two models of this problem, depending on the definition of the dot product of binary vectors: The GF(2) model and the Boolean semiring model. Unlike low rank approximation of a real matrix which can be efficiently solved by Singular Value Decomposition, we show that approximation of a binary matrix is NP-hard, even for k=1. In this paper, our main concern is the problem of Column Subset Selection (CSS), in which the low rank matrix U must be formed by k columns of the data matrix, and we are interested in the approximation ratio achievable by CSS for binary matrices. For the GF(2) model, we show that CSS has approximation ratio bounded by k/2+1+k/(2(2^k-1)) and this is asymptotically tight. For the Boolean model, it turns out that CSS is no longer sufficient to obtain a bound. We then develop a Generalized CSS (GCSS) procedure in which the columns of U are generated from Boolean formulas operating bitwise on selected columns of the data matrix. We show that the approximation ratio achieved by GCSS is bounded by 2^(k-1)+1, and argue that an exponential dependency on k is seems inherent.
Cite as

Chen Dan, Kristoffer Arnsfelt Hansen, He Jiang, Liwei Wang, and Yuchen Zhou. Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 41:1-41:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dan_et_al:LIPIcs.MFCS.2018.41,
  author =	{Dan, Chen and Hansen, Kristoffer Arnsfelt and Jiang, He and Wang, Liwei and Zhou, Yuchen},
  title =	{{Low Rank Approximation of Binary Matrices: Column Subset Selection and Generalizations}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.41},
  URN =		{urn:nbn:de:0030-drops-96239},
  doi =		{10.4230/LIPIcs.MFCS.2018.41},
  annote =	{Keywords: Approximation Algorithms, Low Rank Approximation, Binary Matrices}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.GISCIENCE.2018.35
Multimodal-Transport Collaborative Evacuation Strategies for Urban Serious Emergency Incidents Based on Multi-Sources Spatiotemporal Data (Short Paper)

Authors: Jincheng Jiang, Yang Yue, and Shuai He

Published in: LIPIcs, Volume 114, 10th International Conference on Geographic Information Science (GIScience 2018)

Abstract
When serious emergency events happen in metropolitan cities where pedestrians and vehicles are in high-density, single modal-transport cannot meet the requirements of quick evacuations. Existing mixed modes of transportation lacks spatiotemporal collaborative ability, which cannot work together to accomplish evacuation tasks in a safe and efficient way. It is of great scientific significance and application value for emergency response to adopt multimodal-transport evacuations and improve their spatial-temporal collaboration ability. However, multimodal-transport evacuation strategies for urban serious emergency event are great challenge to be solved. The reasons lie in that: (1) large-scale urban emergency environment are extremely complicated involving many geographical elements (e.g., road, buildings, over-pass, square, hydrographic net, etc.); (2) Evacuated objects are dynamic and hard to be predicted. (3) the distributions of pedestrians and vehicles are unknown. To such issues, this paper reveals both collaborative and competitive mechanisms of multimodal-transport, and further makes global optimal evacuation strategies from the macro-optimization perspective. Considering detailed geographical environment, pedestrian, vehicle and urban rail transit, a multi-objective multi-dynamic-constraints optimization model for multimodal-transport collaborative emergency evacuation is constructed. Take crowd incidents in Shenzhen as example, empirical experiments with real-world data are conducted to evaluate the evacuation strategies and path planning. It is expected to obtain innovative research achievements on theory and method of urban emergency evacuation in serious emergency events. Moreover, this research results provide spatial-temporal decision support for urban emergency response, which is benefit to constructing smart and safe cities.
Cite as

Jincheng Jiang, Yang Yue, and Shuai He. Multimodal-Transport Collaborative Evacuation Strategies for Urban Serious Emergency Incidents Based on Multi-Sources Spatiotemporal Data (Short Paper). In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 35:1-35:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{jiang_et_al:LIPIcs.GISCIENCE.2018.35,
  author =	{Jiang, Jincheng and Yue, Yang and He, Shuai},
  title =	{{Multimodal-Transport Collaborative Evacuation Strategies for Urban Serious Emergency Incidents Based on Multi-Sources Spatiotemporal Data}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{35:1--35:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-083-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{114},
  editor =	{Winter, Stephan and Griffin, Amy and Sester, Monika},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.35},
  URN =		{urn:nbn:de:0030-drops-93630},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.35},
  annote =	{Keywords: evacuation, multimodal-transport, path planning, disaster system modeling, time geography}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.128
Computing Opaque Interior Barriers à la Shermer

Authors: Adrian Dumitrescu, Minghui Jiang, and Csaba D. Tóth

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
The problem of finding a collection of curves of minimum total length that meet all the lines intersecting a given polygon was initiated by Mazurkiewicz in 1916. Such a collection forms an opaque barrier for the polygon. In 1991 Shermer proposed an exponential-time algorithm that computes an interior-restricted barrier made of segments for any given convex n-gon. He conjectured that the barrier found by his algorithm is optimal, however this was refuted recently by Provan et al. Here we give a Shermer like algorithm that computes an interior polygonal barrier whose length is at most 1.7168 times the optimal and that runs in O(n) time. As a byproduct, we also deduce upper and lower bounds on the approximation ratio of Shermer's algorithm.
Cite as

Adrian Dumitrescu, Minghui Jiang, and Csaba D. Tóth. Computing Opaque Interior Barriers à la Shermer. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 128-143, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{dumitrescu_et_al:LIPIcs.APPROX-RANDOM.2014.128,
  author =	{Dumitrescu, Adrian and Jiang, Minghui and T\'{o}th, Csaba D.},
  title =	{{Computing Opaque Interior Barriers \`{a} la Shermer}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{128--143},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.128},
  URN =		{urn:nbn:de:0030-drops-46938},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.128},
  annote =	{Keywords: Opaque barrier, approximation algorithm, isoperimetric inequality}
}
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