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DOI: 10.4230/LIPIcs.ESA.2023.98

Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

Authors: Xiaoming Sun, Jialin Zhang, and Zhijie Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract

Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP). In SMKP, the profits of each subset of elements are specified by a monotone submodular function. The goal is to find a feasible packing of elements over multiple bins (knapsacks) to maximize the profit. Recently, Fairstein et al. [ESA20] proposed a nearly optimal (1-e^{-1}-ε)-approximation algorithm for SMKP. Their algorithm is obtained by combining configuration LP, a grouping technique for bin packing, and the continuous greedy algorithm for submodular maximization. As a result, the algorithm is somewhat sophisticated and inherently randomized. In this paper, we present an arguably simple deterministic combinatorial algorithm for SMKP, which achieves a (1-e^{-1}-ε)-approximation ratio. Our algorithm is based on very different ideas compared with Fairstein et al. [ESA20].

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Xiaoming Sun, Jialin Zhang, and Zhijie Zhang. Simple Deterministic Approximation for Submodular Multiple Knapsack Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 98:1-98:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{sun_et_al:LIPIcs.ESA.2023.98,
  author =	{Sun, Xiaoming and Zhang, Jialin and Zhang, Zhijie},
  title =	{{Simple Deterministic Approximation for Submodular Multiple Knapsack Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{98:1--98:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.98},
  URN =		{urn:nbn:de:0030-drops-187517},
  doi =		{10.4230/LIPIcs.ESA.2023.98},
  annote =	{Keywords: Submodular maximization, knapsack problem, deterministic algorithm}
}

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Short Paper

DOI: 10.4230/LIPIcs.GISCIENCE.2018.72

Scalable Spatial Join for WFS Clients (Short Paper)

Authors: Tian Zhao, Chuanrong Zhang, and Zhijie Zhang

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

Abstract

Web Feature Service (WFS) is a popular Web service for geospatial data, which is represented as sets of features that can be queried using the GetFeature request protocol. However, queries involving spatial joins are not efficiently supported by WFS server implementations such as GeoServer. Performing spatial join at client side is unfortunately expensive and not scalable. In this paper, we propose a simple and yet scalable strategy for performing spatial joins at client side after querying WFS data. Our approach is based on the fact that Web clients of WFS data are often used for query-based visual exploration. In visual exploration, the queried spatial objects can be filtered for a particular zoom level and spatial extent and be simplified before spatial join and still serve their purpose. This way, we can drastically reduce the number of spatial objects retrieved from WFS servers and reduce the computation cost of spatial join, so that even a simple plane-sweep algorithm can yield acceptable performance for interactive applications.

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Tian Zhao, Chuanrong Zhang, and Zhijie Zhang. Scalable Spatial Join for WFS Clients (Short Paper). In 10th International Conference on Geographic Information Science (GIScience 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 114, pp. 72:1-72:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zhao_et_al:LIPIcs.GISCIENCE.2018.72,
  author =	{Zhao, Tian and Zhang, Chuanrong and Zhang, Zhijie},
  title =	{{Scalable Spatial Join for WFS Clients}},
  booktitle =	{10th International Conference on Geographic Information Science (GIScience 2018)},
  pages =	{72:1--72:6},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.GISCIENCE.2018.72},
  URN =		{urn:nbn:de:0030-drops-94007},
  doi =		{10.4230/LIPIcs.GISCIENCE.2018.72},
  annote =	{Keywords: WFS, SPARQL, Spatial Join}
}

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Documents authored by Zhang, Zhijie

Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

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Scalable Spatial Join for WFS Clients (Short Paper)

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