18 Search Results for "Panigrahi, Debmalya"

Document
DOI: 10.4230/DagRep.13.10.76
Graph Algorithms: Cuts, Flows, and Network Design (Dagstuhl Seminar 23422)

Authors: Jason Li, Debmalya Panigrahi, Laura Sanita, and Thatchaphol Saranurak

Published in: Dagstuhl Reports, Volume 13, Issue 10 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23422 "Graph Algorithms: Cuts, Flows, and Network Design". This seminar brought 25 leading researchers in graph algorithms together for a discussion of the recent progress and challenges in two areas: the design of fast algorithm for fundamental flow/cut problems and the design of approximation algorithms for basic network design problems. The seminar included several talks of varying lengths, a panel discussion, and an open problem session. In addition, sufficient time was set aside for research discussions and collaborations.
Cite as

Jason Li, Debmalya Panigrahi, Laura Sanita, and Thatchaphol Saranurak. Graph Algorithms: Cuts, Flows, and Network Design (Dagstuhl Seminar 23422). In Dagstuhl Reports, Volume 13, Issue 10, pp. 76-89, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{li_et_al:DagRep.13.10.76,
  author =	{Li, Jason and Panigrahi, Debmalya and Sanita, Laura and Saranurak, Thatchaphol},
  title =	{{Graph Algorithms: Cuts, Flows, and Network Design (Dagstuhl Seminar 23422)}},
  pages =	{76--89},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{10},
  editor =	{Li, Jason and Panigrahi, Debmalya and Sanita, Laura and Saranurak, Thatchaphol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.10.76},
  URN =		{urn:nbn:de:0030-drops-198357},
  doi =		{10.4230/DagRep.13.10.76},
  annote =	{Keywords: approximation, graph algorithm, maximum flow, minimum cut, network design}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.12
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)

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@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-dev.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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.43
A General Framework for Learning-Augmented Online Allocation

Authors: Ilan Reuven Cohen and Debmalya Panigrahi

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Online allocation is a broad class of problems where items arriving online have to be allocated to agents who have a fixed utility/cost for each assigned item so to maximize/minimize some objective. This framework captures a broad range of fundamental problems such as the Santa Claus problem (maximizing minimum utility), Nash welfare maximization (maximizing geometric mean of utilities), makespan minimization (minimizing maximum cost), minimization of 𝓁_p-norms, and so on. We focus on divisible items (i.e., fractional allocations) in this paper. Even for divisible items, these problems are characterized by strong super-constant lower bounds in the classical worst-case online model. In this paper, we study online allocations in the learning-augmented setting, i.e., where the algorithm has access to some additional (machine-learned) information about the problem instance. We introduce a general algorithmic framework for learning-augmented online allocation that produces nearly optimal solutions for this broad range of maximization and minimization objectives using only a single learned parameter for every agent. As corollaries of our general framework, we improve prior results of Lattanzi et al. (SODA 2020) and Li and Xian (ICML 2021) for learning-augmented makespan minimization, and obtain the first learning-augmented nearly-optimal algorithms for the other objectives such as Santa Claus, Nash welfare, 𝓁_p-minimization, etc. We also give tight bounds on the resilience of our algorithms to errors in the learned parameters, and study the learnability of these parameters.
Cite as

Ilan Reuven Cohen and Debmalya Panigrahi. A General Framework for Learning-Augmented Online Allocation. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.ICALP.2023.43,
  author =	{Cohen, Ilan Reuven and Panigrahi, Debmalya},
  title =	{{A General Framework for Learning-Augmented Online Allocation}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{43:1--43:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.43},
  URN =		{urn:nbn:de:0030-drops-180952},
  doi =		{10.4230/LIPIcs.ICALP.2023.43},
  annote =	{Keywords: Algorithms with predictions, Scheduling algorithms, Online algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.23
Online Paging with Heterogeneous Cache Slots

Authors: Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
It is natural to generalize the online k-Server problem by allowing each request to specify not only a point p, but also a subset S of servers that may serve it. To initiate a systematic study of this generalization, we focus on uniform and star metrics. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a page p, but also a subset S of cache slots, and is satisfied by having a copy of p in some slot in S. We call this problem Slot-Heterogenous Paging. In realistic settings only certain subsets of cache slots or servers would appear in requests. Therefore we parameterize the problem by specifying a family 𝒮 ⊆ 2^[k] of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache size k and family 𝒮. If all request sets are allowed (𝒮 = 2^[k]), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard Paging (𝒮 = {[k]}). As a function of |𝒮| and k, the optimal deterministic ratio is polynomial: at most O(k²|𝒮|) and at least Ω(√{|𝒮|}). For any laminar family {𝒮} of height h, the optimal ratios are O(hk) (deterministic) and O(h²log k) (randomized). The special case that we call All-or-One Paging extends standard Paging by allowing each request to specify a specific slot to put the requested page in. For All-or-One Paging the optimal competitive ratios are Θ(k) (deterministic) and Θ(log k) (randomized), while the offline problem is NP-hard. We extend the deterministic upper bound to the weighted variant of All-or-One Paging (a generalization of standard Weighted Paging), showing that it is also Θ(k). Some results for the laminar case are shown via a reduction to the generalization of Paging in which each request specifies a set P of pages, and is satisfied by fetching any page from P into the cache. The optimal ratios for the latter problem (with laminar family of height h) are at most hk (deterministic) and hH_k (randomized).
Cite as

Marek Chrobak, Samuel Haney, Mehraneh Liaee, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, and Neal E. Young. Online Paging with Heterogeneous Cache Slots. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chrobak_et_al:LIPIcs.STACS.2023.23,
  author =	{Chrobak, Marek and Haney, Samuel and Liaee, Mehraneh and Panigrahi, Debmalya and Rajaraman, Rajmohan and Sundaram, Ravi and Young, Neal E.},
  title =	{{Online Paging with Heterogeneous Cache Slots}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{23:1--23:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.23},
  URN =		{urn:nbn:de:0030-drops-176759},
  doi =		{10.4230/LIPIcs.STACS.2023.23},
  annote =	{Keywords: Caching and paging algorithms, k-server, weighted paging, laminar family}
}
Document
DOI: 10.4230/LIPIcs.CCC.2021.28
Quantum Complexity of Minimum Cut

Authors: Simon Apers and Troy Lee

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract
The minimum cut problem in an undirected and weighted graph G is to find the minimum total weight of a set of edges whose removal disconnects G. We completely characterize the quantum query and time complexity of the minimum cut problem in the adjacency matrix model. If G has n vertices and edge weights at least 1 and at most τ, we give a quantum algorithm to solve the minimum cut problem using Õ(n^{3/2}√{τ}) queries and time. Moreover, for every integer 1 ≤ τ ≤ n we give an example of a graph G with edge weights 1 and τ such that solving the minimum cut problem on G requires Ω(n^{3/2}√{τ}) queries to the adjacency matrix of G. These results contrast with the classical randomized case where Ω(n²) queries to the adjacency matrix are needed in the worst case even to decide if an unweighted graph is connected or not. In the adjacency array model, when G has m edges the classical randomized complexity of the minimum cut problem is ̃ Θ(m). We show that the quantum query and time complexity are Õ(√{mnτ}) and Õ(√{mnτ} + n^{3/2}), respectively, where again the edge weights are between 1 and τ. For dense graphs we give lower bounds on the quantum query complexity of Ω(n^{3/2}) for τ > 1 and Ω(τ n) for any 1 ≤ τ ≤ n. Our query algorithm uses a quantum algorithm for graph sparsification by Apers and de Wolf (FOCS 2020) and results on the structure of near-minimum cuts by Kawarabayashi and Thorup (STOC 2015) and Rubinstein, Schramm and Weinberg (ITCS 2018). Our time efficient implementation builds on Karger’s tree packing technique (STOC 1996).
Cite as

Simon Apers and Troy Lee. Quantum Complexity of Minimum Cut. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 28:1-28:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{apers_et_al:LIPIcs.CCC.2021.28,
  author =	{Apers, Simon and Lee, Troy},
  title =	{{Quantum Complexity of Minimum Cut}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{28:1--28:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.28},
  URN =		{urn:nbn:de:0030-drops-143026},
  doi =		{10.4230/LIPIcs.CCC.2021.28},
  annote =	{Keywords: Quantum algorithms, quantum query complexity, minimum cut}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.45
Sparsification of Directed Graphs via Cut Balance

Authors: Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun

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

Abstract
In this paper, we consider the problem of designing cut sparsifiers and sketches for directed graphs. To bypass known lower bounds, we allow the sparsifier/sketch to depend on the balance of the input graph, which smoothly interpolates between undirected and directed graphs. We give nearly matching upper and lower bounds for both for-all (cf. Benczúr and Karger, STOC 1996) and for-each (Andoni et al., ITCS 2016) cut sparsifiers/sketches as a function of cut balance, defined the maximum ratio of the cut value in the two directions of a directed graph (Ene et al., STOC 2016). We also show an interesting application of digraph sparsification via cut balance by using it to give a very short proof of a celebrated maximum flow result of Karger and Levine (STOC 2002).
Cite as

Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun. Sparsification of Directed Graphs via Cut Balance. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cen_et_al:LIPIcs.ICALP.2021.45,
  author =	{Cen, Ruoxu and Cheng, Yu and Panigrahi, Debmalya and Sun, Kevin},
  title =	{{Sparsification of Directed Graphs via Cut Balance}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{45:1--45:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.45},
  URN =		{urn:nbn:de:0030-drops-141143},
  doi =		{10.4230/LIPIcs.ICALP.2021.45},
  annote =	{Keywords: Graph sparsification, directed graphs, cut sketches, space complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.50
Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity

Authors: Chandra Chekuri and Kent Quanrud

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

Abstract
Li and Panigrahi [Jason Li and Debmalya Panigrahi, 2020], in recent work, obtained the first deterministic algorithm for the global minimum cut of a weighted undirected graph that runs in time o(mn). They introduced an elegant and powerful technique to find isolating cuts for a terminal set in a graph via a small number of s-t minimum cut computations. In this paper we generalize their isolating cut approach to the abstract setting of symmetric bisubmodular functions (which also capture symmetric submodular functions). Our generalization to bisubmodularity is motivated by applications to element connectivity and vertex connectivity. Utilizing the general framework and other ideas we obtain significantly faster randomized algorithms for computing global (and subset) connectivity in a number of settings including hypergraphs, element connectivity and vertex connectivity in graphs, and for symmetric submodular functions.
Cite as

Chandra Chekuri and Kent Quanrud. Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chekuri_et_al:LIPIcs.ICALP.2021.50,
  author =	{Chekuri, Chandra and Quanrud, Kent},
  title =	{{Isolating Cuts, (Bi-)Submodularity, and Faster Algorithms for Connectivity}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{50:1--50:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.50},
  URN =		{urn:nbn:de:0030-drops-141199},
  doi =		{10.4230/LIPIcs.ICALP.2021.50},
  annote =	{Keywords: cuts, vertex connectivity, hypergraphs, fast algorithms, submodularity, bisumodularity, lattices, isolating cuts, element connectivity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.70
Universal Algorithms for Clustering Problems

Authors: Arun Ganesh, Bruce M. Maggs, and Debmalya Panigrahi

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

Abstract
This paper presents universal algorithms for clustering problems, including the widely studied k-median, k-means, and k-center objectives. The input is a metric space containing all potential client locations. The algorithm must select k cluster centers such that they are a good solution for any subset of clients that actually realize. Specifically, we aim for low regret, defined as the maximum over all subsets of the difference between the cost of the algorithm’s solution and that of an optimal solution. A universal algorithm’s solution sol for a clustering problem is said to be an (α, β)-approximation if for all subsets of clients C', it satisfies sol(C') ≤ α ⋅ opt(C') + β ⋅ mr, where opt(C') is the cost of the optimal solution for clients C' and mr is the minimum regret achievable by any solution. Our main results are universal algorithms for the standard clustering objectives of k-median, k-means, and k-center that achieve (O(1), O(1))-approximations. These results are obtained via a novel framework for universal algorithms using linear programming (LP) relaxations. These results generalize to other 𝓁_p-objectives and the setting where some subset of the clients are fixed. We also give hardness results showing that (α, β)-approximation is NP-hard if α or β is at most a certain constant, even for the widely studied special case of Euclidean metric spaces. This shows that in some sense, (O(1), O(1))-approximation is the strongest type of guarantee obtainable for universal clustering.
Cite as

Arun Ganesh, Bruce M. Maggs, and Debmalya Panigrahi. Universal Algorithms for Clustering Problems. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 70:1-70:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ganesh_et_al:LIPIcs.ICALP.2021.70,
  author =	{Ganesh, Arun and Maggs, Bruce M. and Panigrahi, Debmalya},
  title =	{{Universal Algorithms for Clustering Problems}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{70:1--70:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.70},
  URN =		{urn:nbn:de:0030-drops-141397},
  doi =		{10.4230/LIPIcs.ICALP.2021.70},
  annote =	{Keywords: universal algorithms, clustering, k-median, k-means, k-center}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.34
Online Two-Dimensional Load Balancing

Authors: Ilan Cohen, Sungjin Im, and Debmalya Panigrahi

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
In this paper, we consider the problem of assigning 2-dimensional vector jobs to identical machines online so to minimize the maximum load on any dimension of any machine. For arbitrary number of dimensions d, this problem is known as vector scheduling, and recent research has established the optimal competitive ratio as O((log d)/(log log d)) (Im et al. FOCS 2015, Azar et al. SODA 2018). But, these results do not shed light on the situation for small number of dimensions, particularly for d = 2 which is of practical interest. In this case, a trivial analysis shows that the classic list scheduling greedy algorithm has a competitive ratio of 3. We show the following improvements over this baseline in this paper: - We give an improved, and tight, analysis of the list scheduling algorithm establishing a competitive ratio of 8/3 for two dimensions. - If the value of opt is known, we improve the competitive ratio to 9/4 using a variant of the classic best fit algorithm for two dimensions. - For any fixed number of dimensions, we design an algorithm that is provably the best possible against a fractional optimum solution. This algorithm provides a proof of concept that we can simulate the optimal algorithm online up to the integrality gap of the natural LP relaxation of the problem.
Cite as

Ilan Cohen, Sungjin Im, and Debmalya Panigrahi. Online Two-Dimensional Load Balancing. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 34:1-34:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cohen_et_al:LIPIcs.ICALP.2020.34,
  author =	{Cohen, Ilan and Im, Sungjin and Panigrahi, Debmalya},
  title =	{{Online Two-Dimensional Load Balancing}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{34:1--34:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.34},
  URN =		{urn:nbn:de:0030-drops-124415},
  doi =		{10.4230/LIPIcs.ICALP.2020.34},
  annote =	{Keywords: Online algorithms, scheduling, multi-dimensional}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.54
Robust Algorithms for TSP and Steiner Tree

Authors: Arun Ganesh, Bruce M. Maggs, and Debmalya Panigrahi

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret, defined as the maximum difference between the solution’s cost and that of an optimal solution in hindsight once the input has been realized. For graph problems in P, such as shortest path and minimum spanning tree, robust polynomial-time algorithms that obtain a constant approximation on regret are known. In this paper, we study robust algorithms for minimizing regret in NP-hard graph optimization problems, and give constant approximations on regret for the classical traveling salesman and Steiner tree problems.
Cite as

Arun Ganesh, Bruce M. Maggs, and Debmalya Panigrahi. Robust Algorithms for TSP and Steiner Tree. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 54:1-54:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ganesh_et_al:LIPIcs.ICALP.2020.54,
  author =	{Ganesh, Arun and Maggs, Bruce M. and Panigrahi, Debmalya},
  title =	{{Robust Algorithms for TSP and Steiner Tree}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{54:1--54:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.54},
  URN =		{urn:nbn:de:0030-drops-124619},
  doi =		{10.4230/LIPIcs.ICALP.2020.54},
  annote =	{Keywords: Robust optimization, Steiner tree, traveling salesman problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.69
Online Algorithms for Weighted Paging with Predictions

Authors: Zhihao Jiang, Debmalya Panigrahi, and Kevin Sun

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
In this paper, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on unweighted paging with predictions. We show that unlike unweighted paging, neither a fixed lookahead nor knowledge of the next request for every page is sufficient information for an algorithm to overcome existing lower bounds in weighted paging. However, a combination of the two, which we call the strong per request prediction (SPRP) model, suffices to give a 2-competitive algorithm. We also explore the question of gracefully degrading algorithms with increasing prediction error, and give both upper and lower bounds for a set of natural measures of prediction error.
Cite as

Zhihao Jiang, Debmalya Panigrahi, and Kevin Sun. Online Algorithms for Weighted Paging with Predictions. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 69:1-69:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jiang_et_al:LIPIcs.ICALP.2020.69,
  author =	{Jiang, Zhihao and Panigrahi, Debmalya and Sun, Kevin},
  title =	{{Online Algorithms for Weighted Paging with Predictions}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{69:1--69:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.69},
  URN =		{urn:nbn:de:0030-drops-124761},
  doi =		{10.4230/LIPIcs.ICALP.2020.69},
  annote =	{Keywords: Online algorithms, paging}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.70
Retracting Graphs to Cycles

Authors: Samuel Haney, Mehraneh Liaee, Bruce M. Maggs, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram

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

Abstract
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices so as to minimize the maximum stretch of any edge, subject to the constraint that the restriction of the mapping to the cycle is the identity map. This problem has its roots in the rich theory of retraction of topological spaces, and has strong ties to well-studied metric embedding problems such as minimum bandwidth and 0-extension. Our first result is an O(min{k, sqrt{n}})-approximation for retracting any graph on n nodes to a cycle with k nodes. We also show a surprising connection to Sperner’s Lemma that rules out the possibility of improving this result using certain natural convex relaxations of the problem. Nevertheless, if the problem is restricted to planar graphs, we show that we can overcome these integrality gaps by giving an optimal combinatorial algorithm, which is the technical centerpiece of the paper. Building on our planar graph algorithm, we also obtain a constant-factor approximation algorithm for retraction of points in the Euclidean plane to a uniform cycle.
Cite as

Samuel Haney, Mehraneh Liaee, Bruce M. Maggs, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram. Retracting Graphs to Cycles. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 70:1-70:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{haney_et_al:LIPIcs.ICALP.2019.70,
  author =	{Haney, Samuel and Liaee, Mehraneh and Maggs, Bruce M. and Panigrahi, Debmalya and Rajaraman, Rajmohan and Sundaram, Ravi},
  title =	{{Retracting Graphs to Cycles}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{70:1--70:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.70},
  URN =		{urn:nbn:de:0030-drops-106462},
  doi =		{10.4230/LIPIcs.ICALP.2019.70},
  annote =	{Keywords: Graph algorithms, Graph embedding, Planar graphs, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2019.6
Efficient Algorithms for Geometric Partial Matching

Authors: Pankaj K. Agarwal, Hsien-Chih Chang, and Allen Xiao

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

Abstract
Let A and B be two point sets in the plane of sizes r and n respectively (assume r <= n), and let k be a parameter. A matching between A and B is a family of pairs in A x B so that any point of A cup B appears in at most one pair. Given two positive integers p and q, we define the cost of matching M to be c(M) = sum_{(a, b) in M}||a-b||_p^q where ||*||_p is the L_p-norm. The geometric partial matching problem asks to find the minimum-cost size-k matching between A and B. We present efficient algorithms for geometric partial matching problem that work for any powers of L_p-norm matching objective: An exact algorithm that runs in O((n + k^2)polylog n) time, and a (1 + epsilon)-approximation algorithm that runs in O((n + k sqrt{k})polylog n * log epsilon^{-1}) time. Both algorithms are based on the primal-dual flow augmentation scheme; the main improvements involve using dynamic data structures to achieve efficient flow augmentations. With similar techniques, we give an exact algorithm for the planar transportation problem running in O(min{n^2, rn^{3/2}}polylog n) time.
Cite as

Pankaj K. Agarwal, Hsien-Chih Chang, and Allen Xiao. Efficient Algorithms for Geometric Partial Matching. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{agarwal_et_al:LIPIcs.SoCG.2019.6,
  author =	{Agarwal, Pankaj K. and Chang, Hsien-Chih and Xiao, Allen},
  title =	{{Efficient Algorithms for Geometric Partial Matching}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{6:1--6:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.6},
  URN =		{urn:nbn:de:0030-drops-104109},
  doi =		{10.4230/LIPIcs.SoCG.2019.6},
  annote =	{Keywords: partial matching, transportation, optimal transport, minimum-cost flow, bichromatic closest pair}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.43
Profit Sharing and Efficiency in Utility Games

Authors: Sreenivas Gollapudi, Kostas Kollias, Debmalya Panigrahi, and Venetia Pliatsika

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We study utility games (Vetta, FOCS 2002) where a set of players join teams to produce social utility, and receive individual utility in the form of payments in return. These games have many natural applications in competitive settings such as labor markets, crowdsourcing, etc. The efficiency of such a game depends on the profit sharing mechanism - the rule that maps utility produced by the players to their individual payments. We study three natural and widely used profit sharing mechanisms - egalitarian or equal sharing, marginal gain or value addition when a player joins, and marginal loss or value depletion when a player leaves. For these settings, we give tight bounds on the price of anarchy, thereby allowing comparison between these popular mechanisms from a (worst case) social welfare perspective.
Cite as

Sreenivas Gollapudi, Kostas Kollias, Debmalya Panigrahi, and Venetia Pliatsika. Profit Sharing and Efficiency in Utility Games. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gollapudi_et_al:LIPIcs.ESA.2017.43,
  author =	{Gollapudi, Sreenivas and Kollias, Kostas and Panigrahi, Debmalya and Pliatsika, Venetia},
  title =	{{Profit Sharing and Efficiency in Utility Games}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.43},
  URN =		{urn:nbn:de:0030-drops-78329},
  doi =		{10.4230/LIPIcs.ESA.2017.43},
  annote =	{Keywords: Price of anarchy, submodular maximization, coverage functions}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.9
Symmetric Interdiction for Matching Problems

Authors: Samuel Haney, Bruce Maggs, Biswaroop Maiti, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
Motivated by denial-of-service network attacks, we introduce the symmetric interdiction model, where both the interdictor and the optimizer are subject to the same constraints of the underlying optimization problem. We give a general framework that relates optimization to symmetric interdiction for a broad class of optimization problems. We then study the symmetric matching interdiction problem - with applications in traffic engineering - in more detail. This problem can be simply stated as follows: find a matching whose removal minimizes the size of the maximum matching in the remaining graph. We show that this problem is APX-hard, and obtain a 3/2-approximation algorithm that improves on the approximation guarantee provided by the general framework.
Cite as

Samuel Haney, Bruce Maggs, Biswaroop Maiti, Debmalya Panigrahi, Rajmohan Rajaraman, and Ravi Sundaram. Symmetric Interdiction for Matching Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{haney_et_al:LIPIcs.APPROX-RANDOM.2017.9,
  author =	{Haney, Samuel and Maggs, Bruce and Maiti, Biswaroop and Panigrahi, Debmalya and Rajaraman, Rajmohan and Sundaram, Ravi},
  title =	{{Symmetric Interdiction for Matching Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.9},
  URN =		{urn:nbn:de:0030-drops-75587},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.9},
  annote =	{Keywords: Approximation algorithms, matching, interdiction Digital Object}
}
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