76 Search Results for "Chekuri, Chandra"

Volume

LIPIcs, Volume 213

41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

FSTTCS 2021, December 15-17, 2021, Virtual Conference

Editors: Mikołaj Bojańczyk and Chandra Chekuri

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.3
Approximating Submodular k-Partition via Principal Partition Sequence

Authors: Karthekeyan Chandrasekaran and Weihang Wang

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

Abstract
In submodular k-partition, the input is a submodular function f:2^V → ℝ_{≥ 0} (given by an evaluation oracle) along with a positive integer k and the goal is to find a partition of the ground set V into k non-empty parts V_1, V_2, …, V_k in order to minimize ∑_{i=1}^k f(V_i). Narayanan, Roy, and Patkar [Narayanan et al., 1996] designed an algorithm for submodular k-partition based on the principal partition sequence and showed that the approximation factor of their algorithm is 2 for the special case of graph cut functions (which was subsequently rediscovered by Ravi and Sinha [R. Ravi and A. Sinha, 2008]). In this work, we study the approximation factor of their algorithm for three subfamilies of submodular functions - namely monotone, symmetric, and posimodular and show the following results: 1) The approximation factor of their algorithm for monotone submodular k-partition is 4/3. This result improves on the 2-factor that was known to be achievable for monotone submodular k-partition via other algorithms. Moreover, our upper bound of 4/3 matches the recently shown lower bound under polynomial number of function evaluation queries [Santiago, 2021]. Our upper bound of 4/3 is also the first improvement beyond 2 for a certain graph partitioning problem that is a special case of monotone submodular k-partition. 2) The approximation factor of their algorithm for symmetric submodular k-partition is 2. This result generalizes their approximation factor analysis beyond graph cut functions. 3) The approximation factor of their algorithm for posimodular submodular k-partition is 2. We also construct an example to show that the approximation factor of their algorithm for arbitrary submodular functions is Ω(n/k).
Cite as

Karthekeyan Chandrasekaran and Weihang Wang. Approximating Submodular k-Partition via Principal Partition Sequence. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chandrasekaran_et_al:LIPIcs.APPROX/RANDOM.2023.3,
  author =	{Chandrasekaran, Karthekeyan and Wang, Weihang},
  title =	{{Approximating Submodular k-Partition via Principal Partition Sequence}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{3:1--3:16},
  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.2023.3},
  URN =		{urn:nbn:de:0030-drops-188284},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.3},
  annote =	{Keywords: Approximation algorithms}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.7
Bicriteria Approximation Algorithms for Priority Matroid Median

Authors: Tanvi Bajpai and Chandra Chekuri

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

Abstract
Fairness considerations have motivated new clustering problems and algorithms in recent years. In this paper we consider the Priority Matroid Median problem which generalizes the Priority k-Median problem that has recently been studied. The input consists of a set of facilities ℱ and a set of clients 𝒞 that lie in a metric space (ℱ ∪ 𝒞,d), and a matroid ℳ = (ℱ,ℐ) over the facilities. In addition, each client j has a specified radius r_j ≥ 0 and each facility i ∈ ℱ has an opening cost f_i > 0. The goal is to choose a subset S ⊆ ℱ of facilities to minimize ∑_{i ∈ ℱ} f_i + ∑_{j ∈ 𝒞} d(j,S) subject to two constraints: (i) S is an independent set in ℳ (that is S ∈ ℐ) and (ii) for each client j, its distance to an open facility is at most r_j (that is, d(j,S) ≤ r_j). For this problem we describe the first bicriteria (c₁,c₂) approximations for fixed constants c₁,c₂: the radius constraints of the clients are violated by at most a factor of c₁ and the objective cost is at most c₂ times the optimum cost. We also improve the previously known bicriteria approximation for the uniform radius setting (r_j : = L ∀ j ∈ 𝒞).
Cite as

Tanvi Bajpai and Chandra Chekuri. Bicriteria Approximation Algorithms for Priority Matroid Median. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bajpai_et_al:LIPIcs.APPROX/RANDOM.2023.7,
  author =	{Bajpai, Tanvi and Chekuri, Chandra},
  title =	{{Bicriteria Approximation Algorithms for Priority Matroid Median}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{7:1--7:22},
  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.2023.7},
  URN =		{urn:nbn:de:0030-drops-188328},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.7},
  annote =	{Keywords: k-median, fair clustering, matroid}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.24
Independent Sets in Elimination Graphs with a Submodular Objective

Authors: Chandra Chekuri and Kent Quanrud

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

Abstract
Maximum weight independent set (MWIS) admits a 1/k-approximation in inductively k-independent graphs [Karhan Akcoglu et al., 2002; Ye and Borodin, 2012] and a 1/(2k)-approximation in k-perfectly orientable graphs [Kammer and Tholey, 2014]. These are a parameterized class of graphs that generalize k-degenerate graphs, chordal graphs, and intersection graphs of various geometric shapes such as intervals, pseudo-disks, and several others [Ye and Borodin, 2012; Kammer and Tholey, 2014]. We consider a generalization of MWIS to a submodular objective. Given a graph G = (V,E) and a non-negative submodular function f: 2^V → ℝ_+, the goal is to approximately solve max_{S ∈ ℐ_G} f(S) where ℐ_G is the set of independent sets of G. We obtain an Ω(1/k)-approximation for this problem in the two mentioned graph classes. The first approach is via the multilinear relaxation framework and a simple contention resolution scheme, and this results in a randomized algorithm with approximation ratio at least 1/e(k+1). This approach also yields parallel (or low-adaptivity) approximations. Motivated by the goal of designing efficient and deterministic algorithms, we describe two other algorithms for inductively k-independent graphs that are inspired by work on streaming algorithms: a preemptive greedy algorithm and a primal-dual algorithm. In addition to being simpler and faster, these algorithms, in the monotone submodular case, yield the first deterministic constant factor approximations for various special cases that have been previously considered such as intersection graphs of intervals, disks and pseudo-disks.
Cite as

Chandra Chekuri and Kent Quanrud. Independent Sets in Elimination Graphs with a Submodular Objective. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chekuri_et_al:LIPIcs.APPROX/RANDOM.2023.24,
  author =	{Chekuri, Chandra and Quanrud, Kent},
  title =	{{Independent Sets in Elimination Graphs with a Submodular Objective}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{24:1--24:22},
  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.2023.24},
  URN =		{urn:nbn:de:0030-drops-188490},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.24},
  annote =	{Keywords: elimination graphs, independent set, submodular maximization, primal-dual}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.56
Convergence to Lexicographically Optimal Base in a (Contra)Polymatroid and Applications to Densest Subgraph and Tree Packing

Authors: Elfarouk Harb, Kent Quanrud, and Chandra Chekuri

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Boob et al. [Boob et al., 2020] described an iterative peeling algorithm called Greedy++ for the Densest Subgraph Problem (DSG) and conjectured that it converges to an optimum solution. Chekuri, Qaunrud and Torres [Chandra Chekuri et al., 2022] extended the algorithm to supermodular density problems (of which DSG is a special case) and proved that the resulting algorithm Super-Greedy++ (and hence also Greedy++) converges. In this paper we revisit the convergence proof and provide a different perspective. This is done via a connection to Fujishige’s quadratic program for finding a lexicographically optimal base in a (contra) polymatroid [Satoru Fujishige, 1980], and a noisy version of the Frank-Wolfe method from convex optimization [Frank and Wolfe, 1956; Jaggi, 2013]. This yields a simpler convergence proof, and also shows a stronger property that Super-Greedy++ converges to the optimal dense decomposition vector, answering a question raised in Harb et al. [Harb et al., 2022]. A second contribution of the paper is to understand Thorup’s work on ideal tree packing and greedy tree packing [Thorup, 2007; Thorup, 2008] via the Frank-Wolfe algorithm applied to find a lexicographically optimum base in the graphic matroid. This yields a simpler and transparent proof. The two results appear disparate but are unified via Fujishige’s result and convex optimization.
Cite as

Elfarouk Harb, Kent Quanrud, and Chandra Chekuri. Convergence to Lexicographically Optimal Base in a (Contra)Polymatroid and Applications to Densest Subgraph and Tree Packing. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 56:1-56:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{harb_et_al:LIPIcs.ESA.2023.56,
  author =	{Harb, Elfarouk and Quanrud, Kent and Chekuri, Chandra},
  title =	{{Convergence to Lexicographically Optimal Base in a (Contra)Polymatroid and Applications to Densest Subgraph and Tree Packing}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{56:1--56:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.56},
  URN =		{urn:nbn:de:0030-drops-187091},
  doi =		{10.4230/LIPIcs.ESA.2023.56},
  annote =	{Keywords: Polymatroid, lexicographically optimum base, densest subgraph, tree packing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.36
Approximation Algorithms for Network Design in Non-Uniform Fault Models

Authors: Chandra Chekuri and Rhea Jain

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

Abstract
Classical network design models, such as the Survivable Network Design problem (SNDP), are (partly) motivated by robustness to faults under the assumption that any subset of edges upto a specific number can fail. We consider non-uniform fault models where the subset of edges that fail can be specified in different ways. Our primary interest is in the flexible graph connectivity model [Adjiashvili, 2013; Adjiashvili et al., 2020; Adjiashvili et al., 2022; Boyd et al., 2023], in which the edge set is partitioned into safe and unsafe edges. Given parameters p,q ≥ 1, the goal is to find a cheap subgraph that remains p-connected even after the failure of q unsafe edges. We also discuss the bulk-robust model [Adjiashvili et al., 2015; Adjiashvili, 2015] and the relative survivable network design model [Dinitz et al., 2022]. While SNDP admits a 2-approximation [K. Jain, 2001], the approximability of problems in these more complex models is much less understood even in special cases. We make two contributions. Our first set of results are in the flexible graph connectivity model. Motivated by a conjecture that a constant factor approximation is feasible when p and q are fixed, we consider two special cases. For the s-t case we obtain an approximation ratio that depends only on p,q whenever p+q > pq/2 which includes (p,2) and (2,q) for all p,q ≥ 1. For the global connectivity case we obtain an O(q) approximation for (2,q), and an O(p) approximation for (p,2) and (p,3) for any p ≥ 1, and for (p,4) when p is even. These are based on an augmentation framework and decomposing the families of cuts that need to be covered into a small number of uncrossable families. Our second result is a poly-logarithmic approximation for a generalization of the bulk-robust model when the "width" of the given instance (the maximum number of edges that can fail in any particular scenario) is fixed. Via this, we derive corresponding approximations for the flexible graph connectivity model and the relative survivable network design model. We utilize a recent framework due to Chen et al. [Chen et al., 2022] that was designed for handling group connectivity.
Cite as

Chandra Chekuri and Rhea Jain. Approximation Algorithms for Network Design in Non-Uniform Fault Models. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chekuri_et_al:LIPIcs.ICALP.2023.36,
  author =	{Chekuri, Chandra and Jain, Rhea},
  title =	{{Approximation Algorithms for Network Design in Non-Uniform Fault Models}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{36:1--36:20},
  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.2023.36},
  URN =		{urn:nbn:de:0030-drops-180885},
  doi =		{10.4230/LIPIcs.ICALP.2023.36},
  annote =	{Keywords: non-uniform faults, network design, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2022.6
Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions

Authors: Calvin Beideman, Karthekeyan Chandrasekaran, Chandra Chekuri, and Chao Xu

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

Abstract
Submodular functions are fundamental to combinatorial optimization. Many interesting problems can be formulated as special cases of problems involving submodular functions. In this work, we consider the problem of approximating symmetric submodular functions everywhere using hypergraph cut functions. Devanur, Dughmi, Schwartz, Sharma, and Singh [Devanur et al., 2013] showed that symmetric submodular functions over n-element ground sets cannot be approximated within (n/8)-factor using a graph cut function and raised the question of approximating them using hypergraph cut functions. Our main result is that there exist symmetric submodular functions over n-element ground sets that cannot be approximated within a o(n^{1/3}/log² n)-factor using a hypergraph cut function. On the positive side, we show that symmetrized concave linear functions and symmetrized rank functions of uniform matroids and partition matroids can be constant-approximated using hypergraph cut functions.
Cite as

Calvin Beideman, Karthekeyan Chandrasekaran, Chandra Chekuri, and Chao Xu. Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{beideman_et_al:LIPIcs.FSTTCS.2022.6,
  author =	{Beideman, Calvin and Chandrasekaran, Karthekeyan and Chekuri, Chandra and Xu, Chao},
  title =	{{Approximate Representation of Symmetric Submodular Functions via Hypergraph Cut Functions}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{6:1--6:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.6},
  URN =		{urn:nbn:de:0030-drops-173986},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.6},
  annote =	{Keywords: Submodular Functions, Hypergraphs, Approximation, Representation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.37
Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver

Authors: Parinya Chalermsook, Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak, Pattara Sukprasert, and Sorrachai Yingchareonthawornchai

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
In the k-edge-connected spanning subgraph (kECSS) problem, our goal is to compute a minimum-cost sub-network that is resilient against up to k link failures: Given an n-node m-edge graph with a cost function on the edges, our goal is to compute a minimum-cost k-edge-connected spanning subgraph. This NP-hard problem generalizes the minimum spanning tree problem and is the "uniform case" of a much broader class of survival network design problems (SNDP). A factor of two has remained the best approximation ratio for polynomial-time algorithms for the whole class of SNDP, even for a special case of 2ECSS. The fastest 2-approximation algorithm is however rather slow, taking O(mn k) time [Khuller, Vishkin, STOC'92]. A faster time complexity of O(n²) can be obtained, but with a higher approximation guarantee of (2k-1) [Gabow, Goemans, Williamson, IPCO'93]. Our main contribution is an algorithm that (1+ε)-approximates the optimal fractional solution in Õ(m/ε²) time (independent of k), which can be turned into a (2+ε) approximation algorithm that runs in time Õ(m/(ε²) + {k²n^{1.5}}/ε²) for (integral) kECSS; this improves the running time of the aforementioned results while keeping the approximation ratio arbitrarily close to a factor of two.
Cite as

Parinya Chalermsook, Chien-Chung Huang, Danupon Nanongkai, Thatchaphol Saranurak, Pattara Sukprasert, and Sorrachai Yingchareonthawornchai. Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chalermsook_et_al:LIPIcs.ICALP.2022.37,
  author =	{Chalermsook, Parinya and Huang, Chien-Chung and Nanongkai, Danupon and Saranurak, Thatchaphol and Sukprasert, Pattara and Yingchareonthawornchai, Sorrachai},
  title =	{{Approximating k-Edge-Connected Spanning Subgraphs via a Near-Linear Time LP Solver}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{37:1--37:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.37},
  URN =		{urn:nbn:de:0030-drops-163785},
  doi =		{10.4230/LIPIcs.ICALP.2022.37},
  annote =	{Keywords: Approximation Algorithms, Data Structures}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSTTCS.2021
LIPIcs, Volume 213, FSTTCS 2021, Complete Volume

Authors: Mikołaj Bojańczyk and Chandra Chekuri

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
LIPIcs, Volume 213, FSTTCS 2021, Complete Volume
Cite as

41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 1-866, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{bojanczyk_et_al:LIPIcs.FSTTCS.2021,
  title =	{{LIPIcs, Volume 213, FSTTCS 2021, Complete Volume}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{1--866},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021},
  URN =		{urn:nbn:de:0030-drops-155102},
  doi =		{10.4230/LIPIcs.FSTTCS.2021},
  annote =	{Keywords: LIPIcs, Volume 213, FSTTCS 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSTTCS.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Mikołaj Bojańczyk and Chandra Chekuri

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bojanczyk_et_al:LIPIcs.FSTTCS.2021.0,
  author =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.0},
  URN =		{urn:nbn:de:0030-drops-155113},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.1
BQP After 28 Years (Invited Talk)

Authors: Scott Aaronson

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
I will discuss the now-ancient question of where BQP, Bounded-Error Quantum Polynomial-Time, fits in among classical complexity classes. After reviewing some basics from the 90s, I will discuss the Forrelation problem that I introduced in 2009 to yield an oracle separation between BQP and PH, and the dramatic completion of that program by Ran Raz and Avishay Tal in 2018. I will then discuss very recent work, with William Kretschmer and DeVon Ingram, which leverages the Raz-Tal theorem, along with a new "quantum-aware" random restriction method, to obtain results that illustrate just how differently BQP can behave from BPP. These include oracles relative to which NP^{BQP} ̸ ⊂ BQP^{PH} - solving a 2005 open problem of Lance Fortnow - and conversely, relative to which BQP^{NP} ̸ ⊂ PH^{BQP}; an oracle relative to which 𝖯 = NP and yet BQP ≠ QCMA; an oracle relative to which NP ⊆ BQP yet PH is infinite; an oracle relative to which 𝖯 = NP≠ BQP = PP; and an oracle relative to which PP = PostBQP ̸ ⊂ QMA^{QMA^{…}}. By popular demand, I will also speculate about the status of BQP in the unrelativized world.
Cite as

Scott Aaronson. BQP After 28 Years (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{aaronson:LIPIcs.FSTTCS.2021.1,
  author =	{Aaronson, Scott},
  title =	{{BQP After 28 Years}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.1},
  URN =		{urn:nbn:de:0030-drops-155124},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.1},
  annote =	{Keywords: quantum computing, complexity theory, oracle separations, circuit lower bounds}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.2
State Complexity of Population Protocols (Invited Talk)

Authors: Javier Esparza

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Population protocols were introduced by Angluin et al. in 2004 to study the theoretical properties of networks of mobile sensors with very limited computational resources. They have also been proposed as a natural computing model, with molecules, cells, or microorganisms playing the role of sensors. In a population protocol an arbitrary number of indistinguishable, finite-state agents interact randomly in pairs to collectively decide if their initial global configuration satisfies a given property. The property is formalized as a predicate that maps each initial configuration to an output, 0 or 1. Starting from an initial configuration, the agents eventually agree to the correct output almost surely, and continue producing it forever. The protocol is said to stabilize to the correct output. It is well known that population protocols can decide exactly the semilinear predicates, or, equivalently, the predicates expressible in Presburger arithmetic. Current research concentrates on investigating the amount of resources needed to decide a given predicate. The standard resources, time and memory, translate for population protocols into expected time to stabilization, usually called parallel runtime, and number of states of each agent. In this talk we concentrate on the latter. A variant of population protocols allows for a leader, a distinguished finite-state agent that is added to the initial configuration and, intuitively, helps the other agents to organize the computation. In the last years my collaborators and I have obtained upper and lower bounds for the state complexity of population protocols with and without a leader. Define the state complexity of a predicate as the minimal number of states of a protocol that decides the predicate, and STATE(η) as the maximum state complexity of the predicates of size at most η, where predicates are encoded as quantifier-free formulas of Presburger arithmetic with coefficients written in binary. Using techniques from the theory of Petri nets and Vector Addition Systems, we have shown that STATE(η) is polynomially bounded, even for leaderless protocols; this improves on the exponential bound given in 2004 by Angluin and collaborators. We have also proved that STATE(η) ∈ Ω(log log η) for leaderless protocols, even for those deciding very simple predicates of the form x ≥ c for some constant c. In the talk I report on these results, and on two very recent, still unpublished results. Modulo the pending peer-review confirmation, the first result shows the existence of leaderless protocols with a polynomial number of states and linear parallel runtime, and the second, due to Leroux, gives a Ω((log log η)^{1/3}) lower bound for protocols with a leader.
Cite as

Javier Esparza. State Complexity of Population Protocols (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{esparza:LIPIcs.FSTTCS.2021.2,
  author =	{Esparza, Javier},
  title =	{{State Complexity of Population Protocols}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.2},
  URN =		{urn:nbn:de:0030-drops-155139},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.2},
  annote =	{Keywords: Population protocols, state complexity, Petri nets}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.3
Approximately Counting Graph Homomorphisms and Retractions (Invited Talk)

Authors: Leslie Ann Goldberg

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
A homomorphism from a graph G to a graph H is a function from the vertices of G to the vertices of H that preserves the edges of G in the sense that every edge of G is mapped to an edge of H. By changing the target graph H, we can capture interesting structures in G. For example, homomorphisms from G to a k-clique H correspond to the proper k-colourings of G. There has been a lot of algorithmic work on the problem of (approximately) counting homomorphisms. The goal is to figure out for which graphs H the problem of approximately counting homomorphisms to H is algorithmically feasible. This talk will survey what is known. Despite much work, there are still plenty of open problems. We will discuss the problem of approximately counting list homomorphisms (where the input specifies, for each vertex of G, the list of vertices of H to which it can be mapped). Because the lists add extra expressibility, it is easier to prove that counting homomorphisms to a particular graph H is intractable. In fact, we have a full trichotomy (joint work with Galanis and Jerrum, 2017). Here, the complexity of homomorphism-counting is related to certain hereditary graph classes. The trichotomy will be explained in the talk - no prior knowledge of the area will be assumed. In more recent work, with Focke and Živn{ý}, we have investigated the complexity of counting retractions to H - this problem falls between homomorphism-counting and list-homomorphism counting. Here we have only a partial classification, which applies to all square-free graphs H. So again, there are plenty of open problems.
Cite as

Leslie Ann Goldberg. Approximately Counting Graph Homomorphisms and Retractions (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goldberg:LIPIcs.FSTTCS.2021.3,
  author =	{Goldberg, Leslie Ann},
  title =	{{Approximately Counting Graph Homomorphisms and Retractions}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.3},
  URN =		{urn:nbn:de:0030-drops-155146},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.3},
  annote =	{Keywords: Graph homomorphisms, counting}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.4
Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk)

Authors: Huijia (Rachel) Lin

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Indistinguishability obfuscation, introduced by Barak et al. [Crypto 2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from the subexponential hardness of three well-founded assumptions. We prove the following. Theorem (Informal) Assume sub-exponential hardness for the following: - the Learning Parity with Noise (LPN) assumption over general prime fields 𝔽_p with polynomially many LPN samples and error rate 1/k^δ, where k is the dimension of the LPN secret, and δ > 0 is any constant; - the existence of a Boolean Pseudo-Random Generator (PRG) in NC⁰ with stretch n^(1+τ), where n is the length of the PRG seed, and τ > 0 is any constant; - the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exist. As a corollary, all cryptographic goals that can be achieved using indistinguishability obfuscation can now be achieved assuming the above three assumptions. This includes fully homomorphic encryption, functional encryption, multiparty non-interactive key-exchange, succinct garbled random access machine, and many others. This is joint work with Aayush Jain (UCLA and NTT Research) and Amit Sahai (UCLA).
Cite as

Huijia (Rachel) Lin. Indistinguishability Obfuscation from Well-Founded Assumptions (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, p. 4:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lin:LIPIcs.FSTTCS.2021.4,
  author =	{Lin, Huijia (Rachel)},
  title =	{{Indistinguishability Obfuscation from Well-Founded Assumptions}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{4:1--4:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.4},
  URN =		{urn:nbn:de:0030-drops-155154},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.4},
  annote =	{Keywords: Cryptography, indistinguishability obfuscation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSTTCS.2021.5
The Complexity of Gradient Descent (Invited Talk)

Authors: Rahul Savani

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
PPAD and PLS are successful classes that capture the complexity of important game-theoretic problems. For example, finding a mixed Nash equilibrium in a bimatrix game is PPAD-complete, and finding a pure Nash equilibrium in a congestion game is PLS-complete. Many important problems, such as solving a Simple Stochastic Game or finding a mixed Nash equilibrium of a congestion game, lie in both classes. It was strongly believed that their intersection, PPAD ∩ PLS, does not have natural complete problems. We show that it does: any problem that lies in both classes can be reduced in polynomial time to the problem of finding a stationary point of a continuously differentiable function on the domain [0,1]². Thus, as PPAD captures problems that can be solved by Lemke-Howson type complementary pivoting algorithms, and PLS captures problems that can be solved by local search, we show that PPAD ∩ PLS exactly captures problems that can be solved by Gradient Descent. This is joint work with John Fearnley, Paul Goldberg, and Alexandros Hollender. It appeared at STOC'21, where it was given a Best Paper Award [Fearnley et al., 2021].
Cite as

Rahul Savani. The Complexity of Gradient Descent (Invited Talk). In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 5:1-5:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{savani:LIPIcs.FSTTCS.2021.5,
  author =	{Savani, Rahul},
  title =	{{The Complexity of Gradient Descent}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{5:1--5:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.5},
  URN =		{urn:nbn:de:0030-drops-155167},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.5},
  annote =	{Keywords: Computational Complexity, Continuous Optimization, TFNP, PPAD, PLS, CLS, UEOPL}
}
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