11 Search Results for "Wang, Di"


Document
Survey
Towards Representing Processes and Reasoning with Process Descriptions on the Web

Authors: Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1


Abstract
We work towards a vocabulary to represent processes and temporal logic specifications as graph-structured data. Different fields use incompatible terminologies for describing essentially the same process-related concepts. In addition, processes can be represented from different perspectives and levels of abstraction: both state-centric and event-centric perspectives offer distinct insights into the underlying processes. In this work, we strive to unify the representation of processes and related concepts by leveraging the power of knowledge graphs. We survey approaches to representing processes and reasoning with process descriptions from different fields and provide a selection of scenarios to help inform the scope of a unified representation of processes. We focus on processes that can be executed and observed via web interfaces. We propose to provide a representation designed to combine state-centric and event-centric perspectives while incorporating temporal querying and reasoning capabilities on temporal logic specifications. A standardised vocabulary and representation for processes and temporal specifications would contribute towards bridging the gap between the terminologies from different fields and fostering the broader application of methods involving temporal logics, such as formal verification and program synthesis.

Cite as

Andreas Harth, Tobias Käfer, Anisa Rula, Jean-Paul Calbimonte, Eduard Kamburjan, and Martin Giese. Towards Representing Processes and Reasoning with Process Descriptions on the Web. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 1:1-1:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{harth_et_al:TGDK.2.1.1,
  author =	{Harth, Andreas and K\"{a}fer, Tobias and Rula, Anisa and Calbimonte, Jean-Paul and Kamburjan, Eduard and Giese, Martin},
  title =	{{Towards Representing Processes and Reasoning with Process Descriptions on the Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:32},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.1},
  URN =		{urn:nbn:de:0030-drops-198583},
  doi =		{10.4230/TGDK.2.1.1},
  annote =	{Keywords: Process modelling, Process ontology, Temporal logic, Web services}
}
Document
Position
Grounding Stream Reasoning Research

Authors: Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1


Abstract
In the last decade, there has been a growing interest in applying AI technologies to implement complex data analytics over data streams. To this end, researchers in various fields have been organising a yearly event called the "Stream Reasoning Workshop" to share perspectives, challenges, and experiences around this topic. In this paper, the previous organisers of the workshops and other community members provide a summary of the main research results that have been discussed during the first six editions of the event. These results can be categorised into four main research areas: The first is concerned with the technological challenges related to handling large data streams. The second area aims at adapting and extending existing semantic technologies to data streams. The third and fourth areas focus on how to implement reasoning techniques, either considering deductive or inductive techniques, to extract new and valuable knowledge from the data in the stream. This summary is written not only to provide a crystallisation of the field, but also to point out distinctive traits of the stream reasoning community. Moreover, it also provides a foundation for future research by enumerating a list of use cases and open challenges, to stimulate others to join this exciting research area.

Cite as

Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer. Grounding Stream Reasoning Research. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 2:1-2:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{bonte_et_al:TGDK.2.1.2,
  author =	{Bonte, Pieter and Calbimonte, Jean-Paul and de Leng, Daniel and Dell'Aglio, Daniele and Della Valle, Emanuele and Eiter, Thomas and Giannini, Federico and Heintz, Fredrik and Schekotihin, Konstantin and Le-Phuoc, Danh and Mileo, Alessandra and Schneider, Patrik and Tommasini, Riccardo and Urbani, Jacopo and Ziffer, Giacomo},
  title =	{{Grounding Stream Reasoning Research}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:47},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.2},
  URN =		{urn:nbn:de:0030-drops-198597},
  doi =		{10.4230/TGDK.2.1.2},
  annote =	{Keywords: Stream Reasoning, Stream Processing, RDF streams, Streaming Linked Data, Continuous query processing, Temporal Logics, High-performance computing, Databases}
}
Document
Position
Standardizing Knowledge Engineering Practices with a Reference Architecture

Authors: Bradley P. Allen and Filip Ilievski

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1


Abstract
Knowledge engineering is the process of creating and maintaining knowledge-producing systems. Throughout the history of computer science and AI, knowledge engineering workflows have been widely used given the importance of high-quality knowledge for reliable intelligent agents. Meanwhile, the scope of knowledge engineering, as apparent from its target tasks and use cases, has been shifting, together with its paradigms such as expert systems, semantic web, and language modeling. The intended use cases and supported user requirements between these paradigms have not been analyzed globally, as new paradigms often satisfy prior pain points while possibly introducing new ones. The recent abstraction of systemic patterns into a boxology provides an opening for aligning the requirements and use cases of knowledge engineering with the systems, components, and software that can satisfy them best, however, this direction has not been explored to date. This paper proposes a vision of harmonizing the best practices in the field of knowledge engineering by leveraging the software engineering methodology of creating reference architectures. We describe how a reference architecture can be iteratively designed and implemented to associate user needs with recurring systemic patterns, building on top of existing knowledge engineering workflows and boxologies. We provide a six-step roadmap that can enable the development of such an architecture, consisting of scope definition, selection of information sources, architectural analysis, synthesis of an architecture based on the information source analysis, evaluation through instantiation, and, ultimately, instantiation into a concrete software architecture. We provide an initial design and outcome of the definition of architectural scope, selection of information sources, and analysis. As the remaining steps of design, evaluation, and instantiation of the architecture are largely use-case specific, we provide a detailed description of their procedures and point to relevant examples. We expect that following through on this vision will lead to well-grounded reference architectures for knowledge engineering, will advance the ongoing initiatives of organizing the neurosymbolic knowledge engineering space, and will build new links to the software architectures and data science communities.

Cite as

Bradley P. Allen and Filip Ilievski. Standardizing Knowledge Engineering Practices with a Reference Architecture. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{allen_et_al:TGDK.2.1.5,
  author =	{Allen, Bradley P. and Ilievski, Filip},
  title =	{{Standardizing Knowledge Engineering Practices with a Reference Architecture}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:23},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.5},
  URN =		{urn:nbn:de:0030-drops-198623},
  doi =		{10.4230/TGDK.2.1.5},
  annote =	{Keywords: knowledge engineering, knowledge graphs, quality attributes, software architectures, sociotechnical systems}
}
Document
Consistency of Automated Market Makers

Authors: Vincent Danos and Weijia Wang

Published in: OASIcs, Volume 110, 4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022)


Abstract
Decentralised Finance has popularised Automated Market Makers (AMMs), but surprisingly little research has been done on their consistency. Can a single attacker extract risk-free revenue from an AMM, regardless of price or other users' behaviour? In this paper, we investigate the consistency of a large class of AMMs, including the most widely used ones, and show that consistency holds.

Cite as

Vincent Danos and Weijia Wang. Consistency of Automated Market Makers. In 4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022). Open Access Series in Informatics (OASIcs), Volume 110, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{danos_et_al:OASIcs.Tokenomics.2022.4,
  author =	{Danos, Vincent and Wang, Weijia},
  title =	{{Consistency of Automated Market Makers}},
  booktitle =	{4th International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2022)},
  pages =	{4:1--4:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-274-7},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{110},
  editor =	{Amoussou-Guenou, Yackolley and Kiayias, Aggelos and Verdier, Marianne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Tokenomics.2022.4},
  URN =		{urn:nbn:de:0030-drops-184217},
  doi =		{10.4230/OASIcs.Tokenomics.2022.4},
  annote =	{Keywords: Automated Market Makers, Decentralised Finance}
}
Document
Generalized Bundled Fragments for First-Order Modal Logic

Authors: Mo Liu, Anantha Padmanabha, R. Ramanujam, and Yanjing Wang

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
When we bundle quantifiers and modalities together (as in ∃x□, ◇∀x etc.) in first-order modal logic (FOML), we get new logical operators whose combinations produce interesting bundled fragments of FOML. It is well-known that finding decidable fragments of FOML is hard, but existing work shows that certain bundled fragments are decidable [Anantha Padmanabha et al., 2018], without any restriction on the arity of predicates, the number of variables, or the modal scope. In this paper, we explore generalized bundles such as ∀x∀y□, ∀x∃y◇ etc., and map the terrain with regard to decidability, presenting both decidability and undecidability results. In particular, we propose the loosely bundled fragment, which is decidable over increasing domains and encompasses all known decidable bundled fragments.

Cite as

Mo Liu, Anantha Padmanabha, R. Ramanujam, and Yanjing Wang. Generalized Bundled Fragments for First-Order Modal Logic. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 70:1-70:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{liu_et_al:LIPIcs.MFCS.2022.70,
  author =	{Liu, Mo and Padmanabha, Anantha and Ramanujam, R. and Wang, Yanjing},
  title =	{{Generalized Bundled Fragments for First-Order Modal Logic}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.70},
  URN =		{urn:nbn:de:0030-drops-168684},
  doi =		{10.4230/LIPIcs.MFCS.2022.70},
  annote =	{Keywords: bundled fragments, first-order modal logic, decidability, tableaux}
}
Document
Invited Talk
Convex Optimization and Dynamic Data Structure (Invited Talk)

Authors: Yin Tat Lee

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
In the last three years, there are many breakthroughs in optimization such as nearly quadratic time algorithms for bipartite matching, linear programming algorithms that are as fast as Ax = b. All of these algorithms are based on a careful combination of optimization techniques and dynamic data structures. In this talk, we will explain the framework underlying all the recent breakthroughs. Joint work with Jan van den Brand, Michael B. Cohen, Sally Dong, Haotian Jiang, Tarun Kathuria, Danupon Nanongkai, Swati Padmanabhan, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang, Sam Chiu-wai Wong, Guanghao Ye, Qiuyi Zhang.

Cite as

Yin Tat Lee. Convex Optimization and Dynamic Data Structure (Invited Talk). In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{lee:LIPIcs.FSTTCS.2020.3,
  author =	{Lee, Yin Tat},
  title =	{{Convex Optimization and Dynamic Data Structure}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-132440},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.3},
  annote =	{Keywords: Convex Optimization, Dynamic Data Structure}
}
Document
The Reeb Graph Edit Distance Is Universal

Authors: Ulrich Bauer, Claudia Landi, and Facundo Mémoli

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal.

Cite as

Ulrich Bauer, Claudia Landi, and Facundo Mémoli. The Reeb Graph Edit Distance Is Universal. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bauer_et_al:LIPIcs.SoCG.2020.15,
  author =	{Bauer, Ulrich and Landi, Claudia and M\'{e}moli, Facundo},
  title =	{{The Reeb Graph Edit Distance Is Universal}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.15},
  URN =		{urn:nbn:de:0030-drops-121730},
  doi =		{10.4230/LIPIcs.SoCG.2020.15},
  annote =	{Keywords: Reeb graphs, topological descriptors, edit distance, interleaving distance}
}
Document
Upward Book Embeddings of st-Graphs

Authors: Carla Binucci, Giordano Da Lozzo, Emilio Di Giacomo, Walter Didimo, Tamara Mchedlidze, and Maurizio Patrignani

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)


Abstract
We study k-page upward book embeddings (kUBEs) of st-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on k pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a kUBE is NP-complete for k >= 3. A hardness result for this problem was previously known only for k = 6 [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on k=2. On the algorithmic side, we present polynomial-time algorithms for testing the existence of 2UBEs of planar st-graphs with branchwidth b and of plane st-graphs whose faces have a special structure. These algorithms run in O(f(b)* n+n^3) time and O(n) time, respectively, where f is a singly-exponential function on b. Moreover, on the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2UBE.

Cite as

Carla Binucci, Giordano Da Lozzo, Emilio Di Giacomo, Walter Didimo, Tamara Mchedlidze, and Maurizio Patrignani. Upward Book Embeddings of st-Graphs. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{binucci_et_al:LIPIcs.SoCG.2019.13,
  author =	{Binucci, Carla and Da Lozzo, Giordano and Di Giacomo, Emilio and Didimo, Walter and Mchedlidze, Tamara and Patrignani, Maurizio},
  title =	{{Upward Book Embeddings of st-Graphs}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.13},
  URN =		{urn:nbn:de:0030-drops-104170},
  doi =		{10.4230/LIPIcs.SoCG.2019.13},
  annote =	{Keywords: Upward Book Embeddings, st-Graphs, SPQR-trees, Branchwidth, Sphere-cut Decomposition}
}
Document
On Grids in Point-Line Arrangements in the Plane

Authors: Mozhgan Mirzaei and Andrew Suk

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)


Abstract
The famous Szemerédi-Trotter theorem states that any arrangement of n points and n lines in the plane determines O(n^{4/3}) incidences, and this bound is tight. In this paper, we prove the following Turán-type result for point-line incidence. Let L_a and L_b be two sets of t lines in the plane and let P={l_a cap l_b : l_a in L_a, l_b in L_b} be the set of intersection points between L_a and L_b. We say that (P, L_a cup L_b) forms a natural t x t grid if |P| =t^2, and conv(P) does not contain the intersection point of some two lines in L_a and does not contain the intersection point of some two lines in L_b. For fixed t > 1, we show that any arrangement of n points and n lines in the plane that does not contain a natural t x t grid determines O(n^{4/3- epsilon}) incidences, where epsilon = epsilon(t)>0. We also provide a construction of n points and n lines in the plane that does not contain a natural 2 x 2 grid and determines at least Omega(n^{1+1/14}) incidences.

Cite as

Mozhgan Mirzaei and Andrew Suk. On Grids in Point-Line Arrangements in the Plane. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 50:1-50:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{mirzaei_et_al:LIPIcs.SoCG.2019.50,
  author =	{Mirzaei, Mozhgan and Suk, Andrew},
  title =	{{On Grids in Point-Line Arrangements in the Plane}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{50:1--50:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.50},
  URN =		{urn:nbn:de:0030-drops-104541},
  doi =		{10.4230/LIPIcs.SoCG.2019.50},
  annote =	{Keywords: Szemer\'{e}di-Trotter Theorem, Grids, Sidon sets}
}
Document
Unified Acceleration Method for Packing and Covering Problems via Diameter Reduction

Authors: Di Wang, Satish Rao, and Michael W. Mahoney

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


Abstract
In a series of recent breakthroughs, Allen-Zhu and Orecchia [Allen-Zhu/Orecchia, STOC 2015; Allen-Zhu/Orecchia, SODA 2015] leveraged insights from the linear coupling method [Allen-Zhu/Oreccia, arXiv 2014], which is a first-order optimization scheme, to provide improved algorithms for packing and covering linear programs. The result in [Allen-Zhu/Orecchia, STOC 2015] is particularly interesting, as the algorithm for packing LP achieves both width-independence and Nesterov-like acceleration, which was not known to be possible before. Somewhat surprisingly, however, while the dependence of the convergence rate on the error parameter epsilon for packing problems was improved to O(1/epsilon), which corresponds to what accelerated gradient methods are designed to achieve, the dependence for covering problems was only improved to O(1/epsilon^{1.5}), and even that required a different more complicated algorithm, rather than from Nesterov-like acceleration. Given the primal-dual connection between packing and covering problems and since previous algorithms for these very related problems have led to the same epsilon dependence, this discrepancy is surprising, and it leaves open the question of the exact role that the linear coupling is playing in coordinating the complementary gradient and mirror descent step of the algorithm. In this paper, we clarify these issues, illustrating that the linear coupling method can lead to improved O(1/epsilon) dependence for both packing and covering problems in a unified manner, i.e., with the same algorithm and almost identical analysis. Our main technical result is a novel dimension lifting method that reduces the coordinate-wise diameters of the feasible region for covering LPs, which is the key structural property to enable the same Nesterov-like acceleration as in the case of packing LPs. The technique is of independent interest and that may be useful in applying the accelerated linear coupling method to other combinatorial problems.

Cite as

Di Wang, Satish Rao, and Michael W. Mahoney. Unified Acceleration Method for Packing and Covering Problems via Diameter Reduction. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 50:1-50:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{wang_et_al:LIPIcs.ICALP.2016.50,
  author =	{Wang, Di and Rao, Satish and Mahoney, Michael W.},
  title =	{{Unified Acceleration Method for Packing and Covering Problems via Diameter Reduction}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{50:1--50:13},
  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.2016.50},
  URN =		{urn:nbn:de:0030-drops-63308},
  doi =		{10.4230/LIPIcs.ICALP.2016.50},
  annote =	{Keywords: Convex optimization, Accelerated gradient descent, Linear program, Approximation algorithm, Packing and covering}
}
Document
Approximating the Solution to Mixed Packing and Covering LPs in Parallel O˜(epsilon^{-3}) Time

Authors: Michael W. Mahoney, Satish Rao, Di Wang, and Peng Zhang

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


Abstract
We study the problem of approximately solving positive linear programs (LPs). This class of LPs models a wide range of fundamental problems in combinatorial optimization and operations research, such as many resource allocation problems, solving non-negative linear systems, computing tomography, single/multi commodity flows on graphs, etc. For the special cases of pure packing or pure covering LPs, recent result by Allen-Zhu and Orecchia [Allen/Zhu/Orecchia, SODA'15] gives O˜(1/(epsilon^3))-time parallel algorithm, which breaks the longstanding O˜(1/(epsilon^4)) running time bound by the seminal work of Luby and Nisan [Luby/Nisan, STOC'93]. We present new parallel algorithm with running time O˜(1/(epsilon^3)) for the more general mixed packing and covering LPs, which improves upon the O˜(1/(epsilon^4))-time algorithm of Young [Young, FOCS'01; Young, arXiv 2014]. Our work leverages the ideas from both the optimization oriented approach [Allen/Zhu/Orecchia, SODA'15; Wang/Mahoney/Mohan/Rao, arXiv 2015], as well as the more combinatorial approach with phases [Young, FOCS'01; Young, arXiv 2014]. In addition, our algorithm, when directly applied to pure packing or pure covering LPs, gives a improved running time of O˜(1/(epsilon^2)).

Cite as

Michael W. Mahoney, Satish Rao, Di Wang, and Peng Zhang. Approximating the Solution to Mixed Packing and Covering LPs in Parallel O˜(epsilon^{-3}) Time. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


Copy BibTex To Clipboard

@InProceedings{mahoney_et_al:LIPIcs.ICALP.2016.52,
  author =	{Mahoney, Michael W. and Rao, Satish and Wang, Di and Zhang, Peng},
  title =	{{Approximating the Solution to Mixed Packing and Covering LPs in Parallel O˜(epsilon^\{-3\}) Time}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{52:1--52:14},
  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.2016.52},
  URN =		{urn:nbn:de:0030-drops-63335},
  doi =		{10.4230/LIPIcs.ICALP.2016.52},
  annote =	{Keywords: Mixed packing and covering, Linear program, Approximation algorithm, Parallel algorithm}
}
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