28 Search Results for "Gupta, Anupam"


Document
APPROX
Efficient Algorithms and Hardness Results for the Weighted k-Server Problem

Authors: Anupam Gupta, Amit Kumar, and Debmalya Panigrahi

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)


Abstract
In this paper, we study the weighted k-server problem on the uniform metric in both the offline and online settings. We start with the offline setting. In contrast to the (unweighted) k-server problem which has a polynomial-time solution using min-cost flows, there are strong computational lower bounds for the weighted k-server problem, even on the uniform metric. Specifically, we show that assuming the unique games conjecture, there are no polynomial-time algorithms with a sub-polynomial approximation factor, even if we use c-resource augmentation for c < 2. Furthermore, if we consider the natural LP relaxation of the problem, then obtaining a bounded integrality gap requires us to use at least 𝓁 resource augmentation, where 𝓁 is the number of distinct server weights. We complement these results by obtaining a constant-approximation algorithm via LP rounding, with a resource augmentation of (2+ε)𝓁 for any constant ε > 0. In the online setting, an exp(k) lower bound is known for the competitive ratio of any randomized algorithm for the weighted k-server problem on the uniform metric. In contrast, we show that 2𝓁-resource augmentation can bring the competitive ratio down by an exponential factor to only O(𝓁² log 𝓁). Our online algorithm uses the two-stage approach of first obtaining a fractional solution using the online primal-dual framework, and then rounding it online.

Cite as

Anupam Gupta, Amit Kumar, and Debmalya Panigrahi. Efficient Algorithms and Hardness Results for the Weighted k-Server Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.APPROX/RANDOM.2023.12,
  author =	{Gupta, Anupam and Kumar, Amit and Panigrahi, Debmalya},
  title =	{{Efficient Algorithms and Hardness Results for the Weighted k-Server Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.12},
  URN =		{urn:nbn:de:0030-drops-188375},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.12},
  annote =	{Keywords: Online Algorithms, Weighted k-server, Integrality Gap, Hardness}
}
Document
Graph Searching with Predictions

Authors: Siddhartha Banerjee, Vincent Cohen-Addad, Anupam Gupta, and Zhouzi Li

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal while moving only a small distance? This problem seems hopeless, even on trees of bounded degree, unless we give the agent some help. This setting with "help" often arises in exploring large search spaces (e.g., huge game trees) where we assume access to some score/quality function for each node, which we use to guide us towards the goal. In our case, we assume the help comes in the form of distance predictions: each node v provides a prediction f(v) of its distance to the goal vertex. Naturally if these predictions are correct, we can reach the goal along a shortest path. What if the predictions are unreliable and some of them are erroneous? Can we get an algorithm whose performance relates to the error of the predictions? In this work, we consider the problem on trees and give deterministic algorithms whose total movement cost is only O(OPT + Δ ⋅ ERR), where OPT is the distance from the start to the goal vertex, Δ the maximum degree, and the ERR is the total number of vertices whose predictions are erroneous. We show this guarantee is optimal. We then consider a "planning" version of the problem where the graph and predictions are known at the beginning, so the agent can use this global information to devise a search strategy of low cost. For this planning version, we go beyond trees and give an algorithms which gets good performance on (weighted) graphs with bounded doubling dimension.

Cite as

Siddhartha Banerjee, Vincent Cohen-Addad, Anupam Gupta, and Zhouzi Li. Graph Searching with Predictions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{banerjee_et_al:LIPIcs.ITCS.2023.12,
  author =	{Banerjee, Siddhartha and Cohen-Addad, Vincent and Gupta, Anupam and Li, Zhouzi},
  title =	{{Graph Searching with Predictions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.12},
  URN =		{urn:nbn:de:0030-drops-175158},
  doi =		{10.4230/LIPIcs.ITCS.2023.12},
  annote =	{Keywords: Algorithms with predictions, network algorithms, graph search}
}
Document
Invited Talk
Algorithms for Uncertain Environments: Going Beyond the Worst-Case (Invited Talk)

Authors: Anupam Gupta

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)


Abstract
Analyzing the performance of algorithms in both the worst case and the average case are cornerstones of computer science: these are two different ways to understand how well algorithms perform. Over the past two decades, there has been a concerted effort to understand the performance of algorithms in models that go beyond these two extremes. In this talk I will discuss some of the proposed models and approaches, particularly for problems related to online algorithms, where decisions must be made sequentially without knowing future portions of the input.

Cite as

Anupam Gupta. Algorithms for Uncertain Environments: Going Beyond the Worst-Case (Invited Talk). In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{gupta:LIPIcs.FSTTCS.2022.1,
  author =	{Gupta, Anupam},
  title =	{{Algorithms for Uncertain Environments: Going Beyond the Worst-Case}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.1},
  URN =		{urn:nbn:de:0030-drops-173933},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.1},
  annote =	{Keywords: Optimization under Uncertainty, Online Algorithms, Beyond Worst Case Analysis}
}
Document
Probing to Minimize

Authors: Weina Wang, Anupam Gupta, and Jalani K. Williams

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing problems are well-studied. On the other hand, few techniques are known for minimizing the objective, especially in the adaptive setting, where information about the random objective is revealed during the set-selection process and allowed to influence it. For minimization problems in particular, incorporating adaptivity can have a considerable effect on performance. In this work, we seek approximation algorithms that compare well to the optimal adaptive policy. We develop new techniques for adaptive minimization, applying them to a few problems of interest. The core technique we develop here is an approximate reduction from an adaptive expectation minimization problem to a set of adaptive probability minimization problems which we call threshold problems. By providing near-optimal solutions to these threshold problems, we obtain bicriteria adaptive policies. We apply this method to obtain an adaptive approximation algorithm for the Min-Element problem, where the goal is to adaptively pick random variables to minimize the expected minimum value seen among them, subject to a knapsack constraint. This partially resolves an open problem raised in [Goel et al., 2010]. We further consider three extensions on the Min-Element problem, where our objective is the sum of the smallest k element-weights, or the weight of the min-weight basis of a given matroid, or where the constraint is not given by a knapsack but by a matroid constraint. For all three of the variations we explore, we develop adaptive approximation algorithms for their corresponding threshold problems, and prove their near-optimality via coupling arguments.

Cite as

Weina Wang, Anupam Gupta, and Jalani K. Williams. Probing to Minimize. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 120:1-120:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{wang_et_al:LIPIcs.ITCS.2022.120,
  author =	{Wang, Weina and Gupta, Anupam and Williams, Jalani K.},
  title =	{{Probing to Minimize}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{120:1--120:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.120},
  URN =		{urn:nbn:de:0030-drops-157169},
  doi =		{10.4230/LIPIcs.ITCS.2022.120},
  annote =	{Keywords: approximation algorithms, stochastic probing, minimization}
}
Document
APPROX
Bag-Of-Tasks Scheduling on Related Machines

Authors: Anupam Gupta, Amit Kumar, and Sahil Singla

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)


Abstract
We consider online scheduling to minimize weighted completion time on related machines, where each job consists of several tasks that can be concurrently executed. A job gets completed when all its component tasks finish. We obtain an O(K³ log² K)-competitive algorithm in the non-clairvoyant setting, where K denotes the number of distinct machine speeds. The analysis is based on dual-fitting on a precedence-constrained LP relaxation that may be of independent interest.

Cite as

Anupam Gupta, Amit Kumar, and Sahil Singla. Bag-Of-Tasks Scheduling on Related Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.APPROX/RANDOM.2021.3,
  author =	{Gupta, Anupam and Kumar, Amit and Singla, Sahil},
  title =	{{Bag-Of-Tasks Scheduling on Related Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{3:1--3:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.3},
  URN =		{urn:nbn:de:0030-drops-146967},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.3},
  annote =	{Keywords: approximation algorithms, scheduling, bag-of-tasks, related machines}
}
Document
APPROX
Online Directed Spanners and Steiner Forests

Authors: Elena Grigorescu, Young-San Lin, and Kent Quanrud

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)


Abstract
We present online algorithms for directed spanners and directed Steiner forests. These are well-studied network connectivity problems that fall under the unifying framework of online covering and packing linear programming formulations. This framework was developed in the seminal work of Buchbinder and Naor (Mathematics of Operations Research, 34, 2009) and is based on primal-dual techniques. Specifically, our results include the following: - For the pairwise spanner problem, in which the pairs of vertices to be spanned arrive online, we present an efficient randomized algorithm with competitive ratio Õ(n^{4/5}) for graphs with general edge lengths, where n is the number of vertices of the given graph. For graphs with uniform edge lengths, we give an efficient randomized algorithm with competitive ratio Õ(n^{2/3+ε}), and an efficient deterministic algorithm with competitive ratio Õ(k^{1/2+ε}), where k is the number of terminal pairs. To the best of our knowledge, these are the first online algorithms for directed spanners. In the offline version, the current best approximation ratio for uniform edge lengths is Õ(n^{3/5 + ε}), due to Chlamt{á}č, Dinitz, Kortsarz, and Laekhanukit (SODA 2017, TALG 2020). - For the directed Steiner forest problem with uniform costs, in which the pairs of vertices to be connected arrive online, we present an efficient randomized algorithm with competitive ratio Õ(n^{2/3 + ε}). The state-of-the-art online algorithm for general costs is due to Chakrabarty, Ene, Krishnaswamy, and Panigrahi (SICOMP 2018) and is Õ(k^{1/2 + ε})-competitive. In the offline version, the current best approximation ratio with uniform costs is Õ(n^{26/45 + ε}), due to Abboud and Bodwin (SODA 2018). To obtain efficient and competitive online algorithms, we observe that a small modification of the online covering and packing framework by Buchbinder and Naor implies a polynomial-time implementation of the primal-dual approach with separation oracles, which a priori might perform exponentially many calls to the oracle. We convert the online spanner problem into an online covering problem and complete the rounding-step analysis in a problem-specific fashion.

Cite as

Elena Grigorescu, Young-San Lin, and Kent Quanrud. Online Directed Spanners and Steiner Forests. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 5:1-5:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{grigorescu_et_al:LIPIcs.APPROX/RANDOM.2021.5,
  author =	{Grigorescu, Elena and Lin, Young-San and Quanrud, Kent},
  title =	{{Online Directed Spanners and Steiner Forests}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{5:1--5:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.5},
  URN =		{urn:nbn:de:0030-drops-146987},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.5},
  annote =	{Keywords: online directed pairwise spanners, online directed Steiner forests, online covering/packing linear programming, primal-dual approach}
}
Document
Track A: Algorithms, Complexity and Games
Structural Iterative Rounding for Generalized k-Median Problems

Authors: Anupam Gupta, Benjamin Moseley, and Rudy Zhou

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
This paper considers approximation algorithms for generalized k-median problems. This class of problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution with a constant number of fractional variables. The algorithm is based on iteratively rounding linear programs, and the main technical innovation comes from understanding the rich structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios 6.994 + ε and 6.387 + ε for k-median with outliers and knapsack median, respectively. These both improve on the best known approximations.

Cite as

Anupam Gupta, Benjamin Moseley, and Rudy Zhou. Structural Iterative Rounding for Generalized k-Median Problems. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 77:1-77:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.ICALP.2021.77,
  author =	{Gupta, Anupam and Moseley, Benjamin and Zhou, Rudy},
  title =	{{Structural Iterative Rounding for Generalized k-Median Problems}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{77:1--77:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.77},
  URN =		{urn:nbn:de:0030-drops-141465},
  doi =		{10.4230/LIPIcs.ICALP.2021.77},
  annote =	{Keywords: approximation algorithms, clustering, linear programming}
}
Document
Online Carpooling Using Expander Decompositions

Authors: Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, and Sahil Singla

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


Abstract
We consider the online carpooling problem: given n vertices, a sequence of edges arrive over time. When an edge e_t = (u_t, v_t) arrives at time step t, the algorithm must orient the edge either as v_t → u_t or u_t → v_t, with the objective of minimizing the maximum discrepancy of any vertex, i.e., the absolute difference between its in-degree and out-degree. Edges correspond to pairs of persons wanting to ride together, and orienting denotes designating the driver. The discrepancy objective then corresponds to every person driving close to their fair share of rides they participate in. In this paper, we design efficient algorithms which can maintain polylog(n,T) maximum discrepancy (w.h.p) over any sequence of T arrivals, when the arriving edges are sampled independently and uniformly from any given graph G. This provides the first polylogarithmic bounds for the online (stochastic) carpooling problem. Prior to this work, the best known bounds were O(√{n log n})-discrepancy for any adversarial sequence of arrivals, or O(log log n)-discrepancy bounds for the stochastic arrivals when G is the complete graph. The technical crux of our paper is in showing that the simple greedy algorithm, which has provably good discrepancy bounds when the arriving edges are drawn uniformly at random from the complete graph, also has polylog discrepancy when G is an expander graph. We then combine this with known expander-decomposition results to design our overall algorithm.

Cite as

Anupam Gupta, Ravishankar Krishnaswamy, Amit Kumar, and Sahil Singla. Online Carpooling Using Expander Decompositions. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.FSTTCS.2020.23,
  author =	{Gupta, Anupam and Krishnaswamy, Ravishankar and Kumar, Amit and Singla, Sahil},
  title =	{{Online Carpooling Using Expander Decompositions}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{23:1--23:14},
  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.2020.23},
  URN =		{urn:nbn:de:0030-drops-132647},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.23},
  annote =	{Keywords: Online Algorithms, Discrepancy Minimization, Carpooling}
}
Document
Service in Your Neighborhood: Fairness in Center Location

Authors: Christopher Jung, Sampath Kannan, and Neil Lutz

Published in: LIPIcs, Volume 156, 1st Symposium on Foundations of Responsible Computing (FORC 2020)


Abstract
When selecting locations for a set of centers, standard clustering algorithms may place unfair burden on some individuals and neighborhoods. We formulate a fairness concept that takes local population densities into account. In particular, given k centers to locate and a population of size n, we define the "neighborhood radius" of an individual i as the minimum radius of a ball centered at i that contains at least n/k individuals. Our objective is to ensure that each individual has a center that is within at most a small constant factor of her neighborhood radius. We present several theoretical results: We show that optimizing this factor is NP-hard; we give an approximation algorithm that guarantees a factor of at most 2 in all metric spaces; and we prove matching lower bounds in some metric spaces. We apply a variant of this algorithm to real-world address data, showing that it is quite different from standard clustering algorithms and outperforms them on our objective function and balances the load between centers more evenly.

Cite as

Christopher Jung, Sampath Kannan, and Neil Lutz. Service in Your Neighborhood: Fairness in Center Location. In 1st Symposium on Foundations of Responsible Computing (FORC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 156, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{jung_et_al:LIPIcs.FORC.2020.5,
  author =	{Jung, Christopher and Kannan, Sampath and Lutz, Neil},
  title =	{{Service in Your Neighborhood: Fairness in Center Location}},
  booktitle =	{1st Symposium on Foundations of Responsible Computing (FORC 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-142-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{156},
  editor =	{Roth, Aaron},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2020.5},
  URN =		{urn:nbn:de:0030-drops-120215},
  doi =		{10.4230/LIPIcs.FORC.2020.5},
  annote =	{Keywords: Fairness, Clustering, Facility Location}
}
Document
Robust Algorithms for the Secretary Problem

Authors: Domagoj Bradac, Anupam Gupta, Sahil Singla, and Goran Zuzic

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)


Abstract
In classical secretary problems, a sequence of n elements arrive in a uniformly random order, and we want to choose a single item, or a set of size K. The random order model allows us to escape from the strong lower bounds for the adversarial order setting, and excellent algorithms are known in this setting. However, one worrying aspect of these results is that the algorithms overfit to the model: they are not very robust. Indeed, if a few "outlier" arrivals are adversarially placed in the arrival sequence, the algorithms perform poorly. E.g., Dynkin’s popular 1/e-secretary algorithm is sensitive to even a single adversarial arrival: if the adversary gives one large bid at the beginning of the stream, the algorithm does not select any element at all. We investigate a robust version of the secretary problem. In the Byzantine Secretary model, we have two kinds of elements: green (good) and red (rogue). The values of all elements are chosen by the adversary. The green elements arrive at times uniformly randomly drawn from [0,1]. The red elements, however, arrive at adversarially chosen times. Naturally, the algorithm does not see these colors: how well can it solve secretary problems? We show that selecting the highest value red set, or the single largest green element is not possible with even a small fraction of red items. However, on the positive side, we show that these are the only bad cases, by giving algorithms which get value comparable to the value of the optimal green set minus the largest green item. (This benchmark reminds us of regret minimization and digital auctions, where we subtract an additive term depending on the "scale" of the problem.) Specifically, we give an algorithm to pick K elements, which gets within (1-ε) factor of the above benchmark, as long as K ≥ poly(ε^{-1} log n). We extend this to the knapsack secretary problem, for large knapsack size K. For the single-item case, an analogous benchmark is the value of the second-largest green item. For value-maximization, we give a poly log^* n-competitive algorithm, using a multi-layered bucketing scheme that adaptively refines our estimates of second-max over time. For probability-maximization, we show the existence of a good randomized algorithm, using the minimax principle. We hope that this work will spur further research on robust algorithms for the secretary problem, and for other problems in sequential decision-making, where the existing algorithms are not robust and often tend to overfit to the model.

Cite as

Domagoj Bradac, Anupam Gupta, Sahil Singla, and Goran Zuzic. Robust Algorithms for the Secretary Problem. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 32:1-32:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{bradac_et_al:LIPIcs.ITCS.2020.32,
  author =	{Bradac, Domagoj and Gupta, Anupam and Singla, Sahil and Zuzic, Goran},
  title =	{{Robust Algorithms for the Secretary Problem}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{32:1--32:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.32},
  URN =		{urn:nbn:de:0030-drops-117171},
  doi =		{10.4230/LIPIcs.ITCS.2020.32},
  annote =	{Keywords: stochastic optimization, robust optimization, secretary problem, matroid secretary, robust secretary}
}
Document
RANDOM
(Near) Optimal Adaptivity Gaps for Stochastic Multi-Value Probing

Authors: Domagoj Bradac, Sahil Singla, and Goran Zuzic

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)


Abstract
Consider a kidney-exchange application where we want to find a max-matching in a random graph. To find whether an edge e exists, we need to perform an expensive test, in which case the edge e appears independently with a known probability p_e. Given a budget on the total cost of the tests, our goal is to find a testing strategy that maximizes the expected maximum matching size. The above application is an example of the stochastic probing problem. In general the optimal stochastic probing strategy is difficult to find because it is adaptive - decides on the next edge to probe based on the outcomes of the probed edges. An alternate approach is to show the adaptivity gap is small, i.e., the best non-adaptive strategy always has a value close to the best adaptive strategy. This allows us to focus on designing non-adaptive strategies that are much simpler. Previous works, however, have focused on Bernoulli random variables that can only capture whether an edge appears or not. In this work we introduce a multi-value stochastic probing problem, which can also model situations where the weight of an edge has a probability distribution over multiple values. Our main technical contribution is to obtain (near) optimal bounds for the (worst-case) adaptivity gaps for multi-value stochastic probing over prefix-closed constraints. For a monotone submodular function, we show the adaptivity gap is at most 2 and provide a matching lower bound. For a weighted rank function of a k-extendible system (a generalization of intersection of k matroids), we show the adaptivity gap is between O(k log k) and k. None of these results were known even in the Bernoulli case where both our upper and lower bounds also apply, thereby resolving an open question of Gupta et al. [Gupta et al., 2017].

Cite as

Domagoj Bradac, Sahil Singla, and Goran Zuzic. (Near) Optimal Adaptivity Gaps for Stochastic Multi-Value Probing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 49:1-49:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{bradac_et_al:LIPIcs.APPROX-RANDOM.2019.49,
  author =	{Bradac, Domagoj and Singla, Sahil and Zuzic, Goran},
  title =	{{(Near) Optimal Adaptivity Gaps for Stochastic Multi-Value Probing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{49:1--49:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.49},
  URN =		{urn:nbn:de:0030-drops-112641},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.49},
  annote =	{Keywords: stochastic programming, adaptivity gaps, stochastic multi-value probing, submodular functions, k-extendible systems, adaptive strategy, matroid intersection}
}
Document
Track A: Algorithms, Complexity and Games
Covering Metric Spaces by Few Trees

Authors: Yair Bartal, Nova Fandina, and Ofer Neiman

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
A tree cover of a metric space (X,d) is a collection of trees, so that every pair x,y in X has a low distortion path in one of the trees. If it has the stronger property that every point x in X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [Yair Bartal et al., 2005; Anupam Gupta et al., 2004; T-H. Hubert Chan et al., 2005; Gupta et al., 2006; Mendel and Naor, 2007], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [S. Arya et al., 1995]. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.

Cite as

Yair Bartal, Nova Fandina, and Ofer Neiman. Covering Metric Spaces by Few Trees. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{bartal_et_al:LIPIcs.ICALP.2019.20,
  author =	{Bartal, Yair and Fandina, Nova and Neiman, Ofer},
  title =	{{Covering Metric Spaces by Few Trees}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.20},
  URN =		{urn:nbn:de:0030-drops-105967},
  doi =		{10.4230/LIPIcs.ICALP.2019.20},
  annote =	{Keywords: tree cover, Ramsey tree cover, probabilistic hierarchical family}
}
Document
Track A: Algorithms, Complexity and Games
Tight FPT Approximations for k-Median and k-Means

Authors: Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, and Jason Li

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
We investigate the fine-grained complexity of approximating the classical k-Median/k-Means clustering problems in general metric spaces. We show how to improve the approximation factors to (1+2/e+epsilon) and (1+8/e+epsilon) respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures.

Cite as

Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, and Jason Li. Tight FPT Approximations for k-Median and k-Means. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{cohenaddad_et_al:LIPIcs.ICALP.2019.42,
  author =	{Cohen-Addad, Vincent and Gupta, Anupam and Kumar, Amit and Lee, Euiwoong and Li, Jason},
  title =	{{Tight FPT Approximations for k-Median and k-Means}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.42},
  URN =		{urn:nbn:de:0030-drops-106182},
  doi =		{10.4230/LIPIcs.ICALP.2019.42},
  annote =	{Keywords: approximation algorithms, fixed-parameter tractability, k-median, k-means, clustering, core-sets}
}
Document
Track A: Algorithms, Complexity and Games
Non-Clairvoyant Precedence Constrained Scheduling

Authors: Naveen Garg, Anupam Gupta, Amit Kumar, and Sahil Singla

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion (the non-clairvoyant setting). Such precedence-constrained scheduling problems routinely arise in map-reduce and large-scale optimization. For minimizing the total weighted completion time, we give a constant-competitive algorithm. And for total weighted flow-time, we give an O(1/epsilon^2)-competitive algorithm under (1+epsilon)-speed augmentation and a natural "no-surprises" assumption on release dates of jobs (which we show is necessary in this context). Our algorithm proceeds by assigning virtual rates to all waiting jobs, including the ones which are dependent on other uncompleted jobs. We then use these virtual rates to decide on the actual rates of minimal jobs (i.e., jobs which do not have dependencies and hence are eligible to run). Interestingly, the virtual rates are obtained by allocating time in a fair manner, using a Eisenberg-Gale-type convex program (which we can solve optimally using a primal-dual scheme). The optimality condition of this convex program allows us to show dual-fitting proofs more easily, without having to guess and hand-craft the duals. This idea of using fair virtual rates may have broader applicability in scheduling problems.

Cite as

Naveen Garg, Anupam Gupta, Amit Kumar, and Sahil Singla. Non-Clairvoyant Precedence Constrained Scheduling. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{garg_et_al:LIPIcs.ICALP.2019.63,
  author =	{Garg, Naveen and Gupta, Anupam and Kumar, Amit and Singla, Sahil},
  title =	{{Non-Clairvoyant Precedence Constrained Scheduling}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.63},
  URN =		{urn:nbn:de:0030-drops-106394},
  doi =		{10.4230/LIPIcs.ICALP.2019.63},
  annote =	{Keywords: Online algorithms, Scheduling, Primal-Dual analysis, Nash welfare}
}
Document
Track A: Algorithms, Complexity and Games
Stochastic Online Metric Matching

Authors: Anupam Gupta, Guru Guruganesh, Binghui Peng, and David Wajc

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)


Abstract
We study the minimum-cost metric perfect matching problem under online i.i.d arrivals. We are given a fixed metric with a server at each of the points, and then requests arrive online, each drawn independently from a known probability distribution over the points. Each request has to be matched to a free server, with cost equal to the distance. The goal is to minimize the expected total cost of the matching. Such stochastic arrival models have been widely studied for the maximization variants of the online matching problem; however, the only known result for the minimization problem is a tight O(log n)-competitiveness for the random-order arrival model. This is in contrast with the adversarial model, where an optimal competitive ratio of O(log n) has long been conjectured and remains a tantalizing open question. In this paper, we show that the i.i.d model admits substantially better algorithms: our main result is an O((log log log n)^2)-competitive algorithm in this model, implying a strict separation between the i.i.d model and the adversarial and random order models. Along the way we give a 9-competitive algorithm for the line and tree metrics - the first O(1)-competitive algorithm for any non-trivial arrival model for these much-studied metrics.

Cite as

Anupam Gupta, Guru Guruganesh, Binghui Peng, and David Wajc. Stochastic Online Metric Matching. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.ICALP.2019.67,
  author =	{Gupta, Anupam and Guruganesh, Guru and Peng, Binghui and Wajc, David},
  title =	{{Stochastic Online Metric Matching}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.67},
  URN =		{urn:nbn:de:0030-drops-106430},
  doi =		{10.4230/LIPIcs.ICALP.2019.67},
  annote =	{Keywords: stochastic, online, online matching, metric matching}
}
  • Refine by Author
  • 21 Gupta, Anupam
  • 9 Kumar, Amit
  • 5 Singla, Sahil
  • 3 Guruganesh, Guru
  • 2 Bradac, Domagoj
  • Show More...

  • Refine by Classification
  • 10 Theory of computation → Online algorithms
  • 3 Theory of computation → Scheduling algorithms
  • 2 Theory of computation → Design and analysis of algorithms
  • 2 Theory of computation → Facility location and clustering
  • 2 Theory of computation → Packing and covering problems
  • Show More...

  • Refine by Keyword
  • 5 Approximation Algorithms
  • 5 approximation algorithms
  • 3 Online Algorithms
  • 3 Scheduling
  • 3 clustering
  • Show More...

  • Refine by Type
  • 28 document

  • Refine by Publication Year
  • 7 2019
  • 4 2018
  • 3 2010
  • 3 2020
  • 3 2021
  • Show More...

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail