Document

**Published in:** LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph G, a distance bound L, and p pairs of vertices (s_1,t_1),...,(s_p,t_p), the objective is to find a minimum-cost subgraph G' such that s_i and t_i have distance at most L in G' (for every i in [p]). Our main result is on the fixed-parameter tractability of this problem for parameter p. We exactly characterize the demand structures that make the problem "easy", and give FPT algorithms for those cases. In all other cases, we show that the problem is W[1]-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W[1]-hard even to approximate.

Amy Babay, Michael Dinitz, and Zeyu Zhang. Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{babay_et_al:LIPIcs.FSTTCS.2018.33, author = {Babay, Amy and Dinitz, Michael and Zhang, Zeyu}, title = {{Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {33:1--33:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-093-4}, ISSN = {1868-8969}, year = {2018}, volume = {122}, editor = {Ganguly, Sumit and Pandya, Paritosh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.33}, URN = {urn:nbn:de:0030-drops-99329}, doi = {10.4230/LIPIcs.FSTTCS.2018.33}, annote = {Keywords: fixed-parameter tractable, network design, shallow-light steiner network, demand graphs} }

Document

Brief Announcement

**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph G, a distance bound L, and p pairs of vertices {(s_i,t_i)}_{i in [p]}, the objective is to find a minimum-cost subgraph G' such that s_i and t_i have distance at most L in G' (for every i in [p]). Our main result is on the fixed-parameter tractability of this problem for parameter p. We exactly characterize the demand structures that make the problem "easy", and give FPT algorithms for those cases. In all other cases, we show that the problem is W[1]-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W[1]-hard even to approximate.

Amy Babay, Michael Dinitz, and Zeyu Zhang. Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 104:1-104:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{babay_et_al:LIPIcs.ICALP.2018.104, author = {Babay, Amy and Dinitz, Michael and Zhang, Zeyu}, title = {{Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {104:1--104:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.104}, URN = {urn:nbn:de:0030-drops-91083}, doi = {10.4230/LIPIcs.ICALP.2018.104}, annote = {Keywords: Shallow-Light, Steiner Network, Fixed-Parameter Tractability} }

Document

**Published in:** LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Given a finite metric space (V,d), an approximate distance oracle is a data structure which, when queried on two points u,v \in V, returns an approximation to the the actual distance between u and v which is within some bounded stretch factor of the true distance. There has been significant work on the tradeoff between the important parameters of approximate distance oracles (and in particular between the size, stretch, and query time), but in this paper we take a different point of view, that of per-instance optimization. If we are given an particular input metric space and stretch bound, can we find the smallest possible approximate distance oracle for that particular input? Since this question is not even well-defined, we restrict our attention to well-known classes of approximate distance oracles, and study whether we can optimize over those classes.
In particular, we give an O(\log n)-approximation to the problem of finding the smallest stretch 3 Thorup-Zwick distance oracle, as well as the problem of finding the smallest P\v{a}tra\c{s}cu-Roditty distance oracle. We also prove a matching \Omega(\log n) lower bound for both problems, and an \Omega(n^{\frac{1}{k}-\frac{1}{2^{k-1}}}) integrality gap for the more general stretch (2k-1) Thorup-Zwick distance oracle. We also consider the problem of approximating the best TZ or PR approximate distance oracle with outliers, and show that more advanced techniques (SDP relaxations in particular) allow us to optimize even in the presence of outliers.

Michael Dinitz and Zeyu Zhang. Approximating Approximate Distance Oracles. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dinitz_et_al:LIPIcs.ITCS.2017.52, author = {Dinitz, Michael and Zhang, Zeyu}, title = {{Approximating Approximate Distance Oracles}}, booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)}, pages = {52:1--52:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-029-3}, ISSN = {1868-8969}, year = {2017}, volume = {67}, editor = {Papadimitriou, Christos H.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.52}, URN = {urn:nbn:de:0030-drops-81692}, doi = {10.4230/LIPIcs.ITCS.2017.52}, annote = {Keywords: distance oracles, approximation algorithms} }

Document

**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

We consider the following document ranking problem: We have a collection of documents, each containing some topics (e.g. sports, politics, economics). We also have a set of users with diverse interests. Assume that user u is interested in a subset I_u of topics. Each user u is also associated with a positive integer K_u,
which indicates that u can be satisfied by any K_u topics in I_u. Each document s contains information for a subset C_s of topics. The objective is to pick one document at a time such that the average satisfying time is minimized, where a user's satisfying time is the first time that at least K_u topics in I_u are covered in the documents selected so far.
Our main result is an O(rho)-approximation algorithm for the problem, where rho is the algorithmic integrality gap of the linear programming relaxation of the set cover instance defined by the documents and topics. This result generalizes the constant approximations for generalized min-sum set cover and ranking with unrelated intents and the logarithmic approximation for the problem of ranking with submodular valuations (when the submodular function is the coverage function), and can be seen as an interpolation between these results. We further extend our model to the case when each user may be interested in more than one sets of topics and when the user's valuation function is XOS, and obtain similar results for these models.

Jian Li and Zeyu Zhang. Ranking with Diverse Intents and Correlated Contents. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 351-362, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{li_et_al:LIPIcs.FSTTCS.2013.351, author = {Li, Jian and Zhang, Zeyu}, title = {{Ranking with Diverse Intents and Correlated Contents}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {351--362}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.351}, URN = {urn:nbn:de:0030-drops-43856}, doi = {10.4230/LIPIcs.FSTTCS.2013.351}, annote = {Keywords: Approximation Algorithm, Diversification, min-sum Set Cover} }

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