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Documents authored by Vaze, Rahul

Document
DOI: 10.4230/LIPIcs.FSTTCS.2023.6
Online Facility Location with Weights and Congestion

Authors: Arghya Chakraborty and Rahul Vaze

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)

Abstract
The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) weighted requests and (2) congestion. Both of these variants are motivated by their applications to real life scenarios and the previously known results on online facility location cannot be directly adapted to analyse them. - Weighted requests: In this variant, each demand request is a pair (x,w) where x is the standard location of the demand while w is the corresponding weight of the request. The cost of servicing request (x,w) at facility F is w⋅ d(x,F). For this variant, given n requests, we present an online algorithm attaining a competitive ratio of 𝒪(log n) in the secretarial model for the weighted requests and show that it is optimal. -Congestion: The congestion variant considers the case when there is a congestion cost that grows with the number of requests served by each facility. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.
Cite as

Arghya Chakraborty and Rahul Vaze. Online Facility Location with Weights and Congestion. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chakraborty_et_al:LIPIcs.FSTTCS.2023.6,
  author =	{Chakraborty, Arghya and Vaze, Rahul},
  title =	{{Online Facility Location with Weights and Congestion}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.6},
  URN =		{urn:nbn:de:0030-drops-193797},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.6},
  annote =	{Keywords: online algorithms, online facility location, probabilistic method, weighted-requests, congestion}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.22
Robust Online Speed Scaling With Deadline Uncertainty

Authors: Goonwanth Reddy and Rahul Vaze

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
A speed scaling problem is considered, where time is divided into slots, and jobs with payoff v arrive at the beginning of the slot with associated deadlines d. Each job takes one slot to be processed, and multiple jobs can be processed by the server in each slot with energy cost g(k) for processing k jobs in one slot. The payoff is accrued by the algorithm only if the job is processed by its deadline. We consider a robust version of this speed scaling problem, where a job on its arrival reveals its payoff v, however, the deadline is hidden to the online algorithm, which could potentially be chosen adversarially and known to the optimal offline algorithm. The objective is to derive a robust (to deadlines) and optimal online algorithm that achieves the best competitive ratio. We propose an algorithm (called min-LCR) and show that it is an optimal online algorithm for any convex energy cost function g(.). We do so without actually evaluating the optimal competitive ratio, and give a general proof that works for any convex g, which is rather novel. For the popular choice of energy cost function g(k) = k^alpha, alpha >= 2, we give concrete bounds on the competitive ratio of the algorithm, which ranges between 2.618 and 3 depending on the value of alpha. The best known online algorithm for the same problem, but where deadlines are revealed to the online algorithm has competitive ratio of 2 and a lower bound of sqrt{2}. Thus, importantly, lack of deadline knowledge does not make the problem degenerate, and the effect of deadline information on the optimal competitive ratio is limited.
Cite as

Goonwanth Reddy and Rahul Vaze. Robust Online Speed Scaling With Deadline Uncertainty. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{reddy_et_al:LIPIcs.APPROX-RANDOM.2018.22,
  author =	{Reddy, Goonwanth and Vaze, Rahul},
  title =	{{Robust Online Speed Scaling With Deadline Uncertainty}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.22},
  URN =		{urn:nbn:de:0030-drops-94269},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.22},
  annote =	{Keywords: Online Algorithms, Speed Scaling, Greedy Algorithms, Scheduling}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.30
The Adwords Problem with Strict Capacity Constraints

Authors: Umang Bhaskar, Ajil Jalal, and Rahul Vaze

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
We study an online assignment problem where the offline servers have capacities, and the objective is to obtain a maximum-weight assignment of requests that arrive online. The weight of edges incident to any server can be at most the server capacity. Our problem is related to the adwords problem, where the assignment to a server is allowed to exceed its capacity. In many applications, however, server capacities are strict and partially-served requests are of no use, motivating the problem we study. While no deterministic algorithm can be competitive in general for this problem, we give an algorithm with competitive ratio that depends on the ratio of maximum weight of any edge to the capacity of the server it is incident to. If this ratio is 1/2, our algorithm is tight. Further, we give a randomized algorithm that is 6-competitive in expectation for the general problem. Most previous work on the problem and its variants assumes that the edge weights are much smaller than server capacities. Our guarantee, in contrast, does not require any assumptions about job weights. We also give improved lower bounds for both deterministic and randomized algorithms. For the special case of parallel servers, we show that a load-balancing algorithm is tight and near-optimal.
Cite as

Umang Bhaskar, Ajil Jalal, and Rahul Vaze. The Adwords Problem with Strict Capacity Constraints. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 30:1-30:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bhaskar_et_al:LIPIcs.FSTTCS.2016.30,
  author =	{Bhaskar, Umang and Jalal, Ajil and Vaze, Rahul},
  title =	{{The Adwords Problem with Strict Capacity Constraints}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.30},
  URN =		{urn:nbn:de:0030-drops-68651},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.30},
  annote =	{Keywords: Online Algorithms, Adwords, Budgeted Matching, Greedy Algorithms}
}
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