17 Search Results for "Bhattacharya, Sayan"

Document
DOI: 10.4230/LIPIcs.CCC.2024.7
Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.
Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.6
Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces

Authors: Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, and Joachim Spoerhase

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the well-studied Robust (k,z)-Clustering problem, which generalizes the classic k-Median, k-Means, and k-Center problems and arises in the domains of robust optimization [Anthony, Goyal, Gupta, Nagarajan, Math. Oper. Res. 2010] and in algorithmic fairness [Abbasi, Bhaskara, Venkatasubramanian, 2021 & Ghadiri, Samadi, Vempala, 2022]. Given a constant z ≥ 1, the input to Robust (k,z)-Clustering is a set P of n points in a metric space (M,δ), a weight function w: P → ℝ_{≥ 0} and a positive integer k. Further, each point belongs to one (or more) of the m many different groups S_1,S_2,…,S_m ⊆ P. Our goal is to find a set X of k centers such that max_{i ∈ [m]} ∑_{p ∈ S_i} w(p) δ(p,X)^z is minimized. Complementing recent work on this problem, we give a comprehensive understanding of the parameterized approximability of the problem in geometric spaces where the parameter is the number k of centers. We prove the following results: [(i)] 1) For a universal constant η₀ > 0.0006, we devise a 3^z(1-η₀)-factor FPT approximation algorithm for Robust (k,z)-Clustering in discrete high-dimensional Euclidean spaces where the set of potential centers is finite. This shows that the lower bound of 3^z for general metrics [Goyal, Jaiswal, Inf. Proc. Letters, 2023] no longer holds when the metric has geometric structure. 2) We show that Robust (k,z)-Clustering in discrete Euclidean spaces is (√{3/2}- o(1))-hard to approximate for FPT algorithms, even if we consider the special case k-Center in logarithmic dimensions. This rules out a (1+ε)-approximation algorithm running in time f(k,ε)poly(m,n) (also called efficient parameterized approximation scheme or EPAS), giving a striking contrast with the recent EPAS for the continuous setting where centers can be placed anywhere in the space [Abbasi et al., FOCS'23]. 3) However, we obtain an EPAS for Robust (k,z)-Clustering in discrete Euclidean spaces when the dimension is sublogarithmic (for the discrete problem, earlier work [Abbasi et al., FOCS'23] provides an EPAS only in dimension o(log log n)). Our EPAS works also for metrics of sub-logarithmic doubling dimension.
Cite as

Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, and Joachim Spoerhase. Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abbasi_et_al:LIPIcs.ICALP.2024.6,
  author =	{Abbasi, Fateme and Banerjee, Sandip and Byrka, Jaros{\l}aw and Chalermsook, Parinya and Gadekar, Ameet and Khodamoradi, Kamyar and Marx, D\'{a}niel and Sharma, Roohani and Spoerhase, Joachim},
  title =	{{Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.6},
  URN =		{urn:nbn:de:0030-drops-201494},
  doi =		{10.4230/LIPIcs.ICALP.2024.6},
  annote =	{Keywords: Clustering, approximation algorithms, parameterized complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.40
Streaming Edge Coloring with Subquadratic Palette Size

Authors: Shiri Chechik, Doron Mukhtar, and Tianyi Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper, we study the problem of computing an edge-coloring in the (one-pass) W-streaming model. In this setting, the edges of an n-node graph arrive in an arbitrary order to a machine with a relatively small space, and the goal is to design an algorithm that outputs, as a stream, a proper coloring of the edges using the fewest possible number of colors. Behnezhad et al. [Behnezhad et al., 2019] devised the first non-trivial algorithm for this problem, which computes in Õ(n) space a proper O(Δ²)-coloring w.h.p. (here Δ is the maximum degree of the graph). Subsequent papers improved upon this result, where latest of them [Ansari et al., 2022] showed that it is possible to deterministically compute an O(Δ²/s)-coloring in O(ns) space. However, none of the improvements succeeded in reducing the number of colors to O(Δ^{2-ε}) while keeping the same space bound of Õ(n). In particular, no progress was made on the question of whether computing an O(Δ)-coloring is possible with roughly O(n) space, which was stated in [Behnezhad et al., 2019] to be an interesting open problem. In this paper we bypass the quadratic bound by presenting a new randomized Õ(n)-space algorithm that uses Õ(Δ^{1.5}) colors.
Cite as

Shiri Chechik, Doron Mukhtar, and Tianyi Zhang. Streaming Edge Coloring with Subquadratic Palette Size. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 40:1-40:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2024.40,
  author =	{Chechik, Shiri and Mukhtar, Doron and Zhang, Tianyi},
  title =	{{Streaming Edge Coloring with Subquadratic Palette Size}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{40:1--40:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.40},
  URN =		{urn:nbn:de:0030-drops-201831},
  doi =		{10.4230/LIPIcs.ICALP.2024.40},
  annote =	{Keywords: graph algorithms, streaming algorithms, edge coloring}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.19
Sublinear Algorithms for TSP via Path Covers

Authors: Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related maximum path cover problem, which asks for a collection of vertex disjoint paths that include the maximum number of edges. We show that for any fixed ε > 0, there is an algorithm that (1/2 - ε)-approximates the maximum path cover size of an n-vertex graph in Õ(n) time. This improves upon a (3/8-ε)-approximate Õ(n √n)-time algorithm of Chen, Kannan, and Khanna [ICALP'20]. Equipped with our path cover algorithm, we give an Õ(n) time algorithm that estimates the cost of (1,2)-TSP within a factor of (1.5+ε) which is an improvement over a folklore (1.75 + ε)-approximate Õ(n)-time algorithm, as well as a (1.625+ε)-approximate Õ(n√n)-time algorithm of [CHK ICALP'20]. For graphic TSP, we present an Õ(n) algorithm that estimates the cost of graphic TSP within a factor of 1.83 which is an improvement over a 1.92-approximate Õ(n) time algorithm due to [CHK ICALP'20, Behnezhad FOCS'21]. We show that the approximation can be further improved to 1.66 using n^{2-Ω(1)} time. All of our Õ(n) time algorithms are information-theoretically time-optimal up to polylog n factors. Additionally, we show that our approximation guarantees for path cover and (1,2)-TSP hit a natural barrier: We show better approximations require better sublinear time algorithms for the well-studied maximum matching problem.
Cite as

Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Sublinear Algorithms for TSP via Path Covers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{behnezhad_et_al:LIPIcs.ICALP.2024.19,
  author =	{Behnezhad, Soheil and Roghani, Mohammad and Rubinstein, Aviad and Saberi, Amin},
  title =	{{Sublinear Algorithms for TSP via Path Covers}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.19},
  URN =		{urn:nbn:de:0030-drops-201623},
  doi =		{10.4230/LIPIcs.ICALP.2024.19},
  annote =	{Keywords: Sublinear Algorithms, Traveling Salesman Problem, Approximation Algorithm, (1, 2)-TSP, Graphic TSP}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.59
Decremental Matching in General Weighted Graphs

Authors: Aditi Dudeja

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper, we consider the problem of maintaining a (1-ε)-approximate maximum weight matching in a dynamic graph G, while the adversary makes changes to the edges of the graph. In the fully dynamic setting, where both edge insertions and deletions are allowed, Gupta and Peng [Manoj Gupta and Richard Peng, 2013] gave an algorithm for this problem with an update time of Õ_ε(√m). We study a natural relaxation of this problem, namely the decremental model, where the adversary is only allowed to delete edges. For the unweighted version of this problem in general (possibly, non-bipartite) graphs, [Sepehr Assadi et al., 2022] gave a decremental algorithm with update time O_ε(poly(log n)). However, beating Õ_ε(√m) update time remained an open problem for the weighted version in general graphs. In this paper, we bridge the gap between unweighted and weighted general graphs for the decremental setting. We give a O_ε(poly(log n)) update time algorithm that maintains a (1-ε) approximate maximum weight matching under adversarial deletions. Like the decremental algorithm of [Sepehr Assadi et al., 2022], our algorithm is randomized, but works against an adaptive adversary. It also matches the time bound for the unweighted version upto dependencies on ε and a log R factor, where R is the ratio between the maximum and minimum edge weight in G.
Cite as

Aditi Dudeja. Decremental Matching in General Weighted Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dudeja:LIPIcs.ICALP.2024.59,
  author =	{Dudeja, Aditi},
  title =	{{Decremental Matching in General Weighted Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{59:1--59:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.59},
  URN =		{urn:nbn:de:0030-drops-202020},
  doi =		{10.4230/LIPIcs.ICALP.2024.59},
  annote =	{Keywords: Weighted Matching, Dynamic Algorithms, Adaptive Adversary}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.71
Low-Memory Algorithms for Online Edge Coloring

Authors: Prantar Ghosh and Manuel Stoeckl

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
For edge coloring, the online and the W-streaming models seem somewhat orthogonal: the former needs edges to be assigned colors immediately after insertion, typically without any space restrictions, while the latter limits memory to be sublinear in the input size but allows an edge’s color to be announced any time after its insertion. We aim for the best of both worlds by designing small-space online algorithms for edge coloring. Our online algorithms significantly improve upon the memory used by prior ones while achieving an O(1)-competitive ratio. We study the problem under both (adversarial) edge arrivals and vertex arrivals. Under vertex arrivals of any n-node graph with maximum vertex-degree Δ, our online O(Δ)-coloring algorithm uses only semi-streaming space (i.e., Õ(n) space, where the Õ(.) notation hides polylog(n) factors). Under edge arrivals, we obtain an online O(Δ)-coloring in Õ(n√Δ) space. We also achieve a smooth color-space tradeoff: for any t = O(Δ), we get an O(Δt(log²Δ))-coloring in Õ(n√{Δ/t}) space, improving upon the state of the art that used Õ(nΔ/t) space for the same number of colors. The improvements stem from extensive use of random permutations that enable us to avoid previously used colors. Most of our algorithms can be derandomized and extended to multigraphs, where edge coloring is known to be considerably harder than for simple graphs.
Cite as

Prantar Ghosh and Manuel Stoeckl. Low-Memory Algorithms for Online Edge Coloring. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 71:1-71:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghosh_et_al:LIPIcs.ICALP.2024.71,
  author =	{Ghosh, Prantar and Stoeckl, Manuel},
  title =	{{Low-Memory Algorithms for Online Edge Coloring}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{71:1--71:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.71},
  URN =		{urn:nbn:de:0030-drops-202146},
  doi =		{10.4230/LIPIcs.ICALP.2024.71},
  annote =	{Keywords: Edge coloring, streaming model, online algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.120
Caching Connections in Matchings

Authors: Yaniv Sadeh and Haim Kaplan

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a natural combinatorial structure and therefore may find additional applications in theory and practice. In the Caching in Matchings problem our cache consists of k matchings of connections between servers that form a bipartite graph. To cache a connection we insert it into one of the k matchings possibly evicting at most two other connections from this matching. This problem resembles the problem known as Connection Caching [Cohen et al., 2000], where we also cache connections but our only restriction is that they form a graph with bounded degree k. Our results show a somewhat surprising qualitative separation between the problems: The competitive ratio of any online algorithm for caching in matchings must depend on the size of the graph. Specifically, we give a deterministic O(nk) competitive and randomized O(n log k) competitive algorithms for caching in matchings, where n is the number of servers and k is the number of matchings. We also show that the competitive ratio of any deterministic algorithm is Ω(max(n/k,k)) and of any randomized algorithm is Ω(log (n/(k² log k)) ⋅ log k). In particular, the lower bound for randomized algorithms is Ω(log n) regardless of k, and can be as high as Ω(log² n) if k = n^{1/3}, for example. We also show that if we allow the algorithm to use at least 2k-1 matchings compared to k used by the optimum then we match the competitive ratios of connection catching which are independent of n. Interestingly, we also show that even a single extra matching for the algorithm allows to get substantially better bounds.
Cite as

Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120,
  author =	{Sadeh, Yaniv and Kaplan, Haim},
  title =	{{Caching Connections in Matchings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{120:1--120:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.120},
  URN =		{urn:nbn:de:0030-drops-202639},
  doi =		{10.4230/LIPIcs.ICALP.2024.120},
  annote =	{Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.121
Streaming Edge Coloring with Asymptotically Optimal Colors

Authors: Mohammad Saneian and Soheil Behnezhad

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given a graph G, an edge-coloring is an assignment of colors to edges of G such that any two edges sharing an endpoint receive different colors. By Vizing’s celebrated theorem, any graph of maximum degree Δ needs at least Δ and at most (Δ + 1) colors to be properly edge colored. In this paper, we study edge colorings in the streaming setting. The edges arrive one by one in an arbitrary order. The algorithm takes a single pass over the input and must output a solution using a much smaller space than the input size. Since the output of edge coloring is as large as its input, the assigned colors should also be reported in a streaming fashion. The streaming edge coloring problem has been studied in a series of works over the past few years. The main challenge is that the algorithm cannot "remember" all the color assignments that it returns. To ensure the validity of the solution, existing algorithms use many more colors than Vizing’s bound. Namely, in n-vertex graphs, the state-of-the-art algorithm with Õ(n s) space requires O(Δ²/s + Δ) colors. Note, in particular, that for an asymptotically optimal O(Δ) coloring, this algorithm requires Ω(nΔ) space which is as large as the input. Whether such a coloring can be achieved with sublinear space has been left open. In this paper, we answer this question in the affirmative. We present a randomized algorithm that returns an asymptotically optimal O(Δ) edge coloring using Õ(n √{Δ}) space. More generally, our algorithm returns a proper O(Δ^{1.5}/s + Δ) edge coloring with Õ(n s) space, improving prior algorithms for the whole range of s.
Cite as

Mohammad Saneian and Soheil Behnezhad. Streaming Edge Coloring with Asymptotically Optimal Colors. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 121:1-121:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{saneian_et_al:LIPIcs.ICALP.2024.121,
  author =	{Saneian, Mohammad and Behnezhad, Soheil},
  title =	{{Streaming Edge Coloring with Asymptotically Optimal Colors}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{121:1--121:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.121},
  URN =		{urn:nbn:de:0030-drops-202640},
  doi =		{10.4230/LIPIcs.ICALP.2024.121},
  annote =	{Keywords: Streaming, Edge coloring, Adversarial order}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.12
Arboricity-Dependent Algorithms for Edge Coloring

Authors: Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
The problem of edge coloring has been extensively studied over the years. Recently, this problem has received significant attention in the dynamic setting, where we are given a dynamic graph evolving via a sequence of edge insertions and deletions and our objective is to maintain an edge coloring of the graph. Currently, it is not known whether it is possible to maintain a (Δ + O(Δ^(1-μ)))-edge coloring in Õ(1) update time, for any constant μ > 0, where Δ is the maximum degree of the graph. In this paper, we show how to efficiently maintain a (Δ + O(α))-edge coloring in Õ(1) amortized update time, where α is the arboricty of the graph. Thus, we answer this question in the affirmative for graphs of sufficiently small arboricity.
Cite as

Sayan Bhattacharya, Martín Costa, Nadav Panski, and Shay Solomon. Arboricity-Dependent Algorithms for Edge Coloring. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhattacharya_et_al:LIPIcs.SWAT.2024.12,
  author =	{Bhattacharya, Sayan and Costa, Mart{\'\i}n and Panski, Nadav and Solomon, Shay},
  title =	{{Arboricity-Dependent Algorithms for Edge Coloring}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.12},
  URN =		{urn:nbn:de:0030-drops-200524},
  doi =		{10.4230/LIPIcs.SWAT.2024.12},
  annote =	{Keywords: Dynamic Algorithms, Graph Algorithms, Edge Coloring, Arboricity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.17
Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary

Authors: Sayan Bhattacharya, Thatchaphol Saranurak, and Pattara Sukprasert

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Designing dynamic algorithms against an adaptive adversary whose performance match the ones assuming an oblivious adversary is a major research program in the field of dynamic graph algorithms. One of the prominent examples whose oblivious-vs-adaptive gap remains maximally large is the fully dynamic spanner problem; there exist algorithms assuming an oblivious adversary with near-optimal size-stretch trade-off using only polylog(n) update time [Baswana, Khurana, and Sarkar TALG'12; Forster and Goranci STOC'19; Bernstein, Forster, and Henzinger SODA'20], while against an adaptive adversary, even when we allow infinite time and only count recourse (i.e. the number of edge changes per update in the maintained spanner), all previous algorithms with stretch at most log⁵(n) require at least Ω(n) amortized recourse [Ausiello, Franciosa, and Italiano ESA'05]. In this paper, we completely close this gap with respect to recourse by showing algorithms against an adaptive adversary with near-optimal size-stretch trade-off and recourse. More precisely, for any k ≥ 1, our algorithm maintains a (2k-1)-spanner of size O(n^{1+1/k}log n) with O(log n) amortized recourse, which is optimal in all parameters up to a O(log n) factor. As a step toward algorithms with small update time (not just recourse), we show another algorithm that maintains a 3-spanner of size Õ(n^{1.5}) with polylog(n) amortized recourse and simultaneously Õ(√n) worst-case update time.
Cite as

Sayan Bhattacharya, Thatchaphol Saranurak, and Pattara Sukprasert. Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhattacharya_et_al:LIPIcs.ESA.2022.17,
  author =	{Bhattacharya, Sayan and Saranurak, Thatchaphol and Sukprasert, Pattara},
  title =	{{Simple Dynamic Spanners with Near-Optimal Recourse Against an Adaptive Adversary}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.17},
  URN =		{urn:nbn:de:0030-drops-169555},
  doi =		{10.4230/LIPIcs.ESA.2022.17},
  annote =	{Keywords: Algorithms, Dynamic Algorithms, Spanners, Recourse}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.37
Adversarially Robust Coloring for Graph Streams

Authors: Amit Chakrabarti, Prantar Ghosh, and Manuel Stoeckl

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

Abstract
A streaming algorithm is considered to be adversarially robust if it provides correct outputs with high probability even when the stream updates are chosen by an adversary who may observe and react to the past outputs of the algorithm. We grow the burgeoning body of work on such algorithms in a new direction by studying robust algorithms for the problem of maintaining a valid vertex coloring of an n-vertex graph given as a stream of edges. Following standard practice, we focus on graphs with maximum degree at most Δ and aim for colorings using a small number f(Δ) of colors. A recent breakthrough (Assadi, Chen, and Khanna; SODA 2019) shows that in the standard, non-robust, streaming setting, (Δ+1)-colorings can be obtained while using only Õ(n) space. Here, we prove that an adversarially robust algorithm running under a similar space bound must spend almost Ω(Δ²) colors and that robust O(Δ)-coloring requires a linear amount of space, namely Ω(nΔ). We in fact obtain a more general lower bound, trading off the space usage against the number of colors used. From a complexity-theoretic standpoint, these lower bounds provide (i) the first significant separation between adversarially robust algorithms and ordinary randomized algorithms for a natural problem on insertion-only streams and (ii) the first significant separation between randomized and deterministic coloring algorithms for graph streams, since deterministic streaming algorithms are automatically robust. We complement our lower bounds with a suite of positive results, giving adversarially robust coloring algorithms using sublinear space. In particular, we can maintain an O(Δ²)-coloring using Õ(n √Δ) space and an O(Δ³)-coloring using Õ(n) space.
Cite as

Amit Chakrabarti, Prantar Ghosh, and Manuel Stoeckl. Adversarially Robust Coloring for Graph Streams. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 37:1-37:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chakrabarti_et_al:LIPIcs.ITCS.2022.37,
  author =	{Chakrabarti, Amit and Ghosh, Prantar and Stoeckl, Manuel},
  title =	{{Adversarially Robust Coloring for Graph Streams}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{37:1--37:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.37},
  URN =		{urn:nbn:de:0030-drops-156332},
  doi =		{10.4230/LIPIcs.ITCS.2022.37},
  annote =	{Keywords: Data streaming, graph algorithms, graph coloring, lower bounds, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.94
Deterministic Dynamic Matching in Worst-Case Update Time

Authors: Peter Kiss

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

Abstract
We present deterministic algorithms for maintaining a (3/2 + ε) and (2 + ε)-approximate maximum matching in a fully dynamic graph with worst-case update times Ô(√n) and Õ(1) respectively. The fastest known deterministic worst-case update time algorithms for achieving approximation ratio (2 - δ) (for any δ > 0) and (2 + ε) were both shown by Roghani et al. [arXiv'2021] with update times O(n^{3/4}) and O_ε(√n) respectively. We close the gap between worst-case and amortized algorithms for the two approximation ratios as the best deterministic amortized update times for the problem are O_ε(√n) and Õ(1) which were shown in Bernstein and Stein [SODA'2021] and Bhattacharya and Kiss [ICALP'2021] respectively. The algorithm achieving (3/2 + ε) approximation builds on the EDCS concept introduced by the influential paper of Bernstein and Stein [ICALP'2015]. Say that H is a (α, δ)-approximate matching sparsifier if at all times H satisfies that μ(H) ⋅ α + δ ⋅ n ≥ μ(G) (define (α, δ)-approximation similarly for matchings). We show how to maintain a locally damaged version of the EDCS which is a (3/2 + ε, δ)-approximate matching sparsifier. We further show how to reduce the maintenance of an α-approximate maximum matching to the maintenance of an (α, δ)-approximate maximum matching building based on an observation of Assadi et al. [EC'2016]. Our reduction requires an update time blow-up of Ô(1) or Õ(1) and is deterministic or randomized against an adaptive adversary respectively. To achieve (2 + ε)-approximation we improve on the update time guarantee of an algorithm of Bhattacharya and Kiss [ICALP'2021]. In order to achieve both results we explicitly state a method implicitly used in Nanongkai and Saranurak [STOC'2017] and Bernstein et al. [arXiv'2020] which allows to transform dynamic algorithms capable of processing the input in batches to a dynamic algorithms with worst-case update time. Independent Work: Independently and concurrently to our work Grandoni et al. [arXiv'2021] has presented a fully dynamic algorithm for maintaining a (3/2 + ε)-approximate maximum matching with deterministic worst-case update time O_ε(√n).
Cite as

Peter Kiss. Deterministic Dynamic Matching in Worst-Case Update Time. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 94:1-94:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kiss:LIPIcs.ITCS.2022.94,
  author =	{Kiss, Peter},
  title =	{{Deterministic Dynamic Matching in Worst-Case Update Time}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{94:1--94:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.94},
  URN =		{urn:nbn:de:0030-drops-156909},
  doi =		{10.4230/LIPIcs.ITCS.2022.94},
  annote =	{Keywords: Dynamic Algorithms, Matching, Approximate Matching, EDCS}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.111
Beating the Folklore Algorithm for Dynamic Matching

Authors: Mohammad Roghani, Amin Saberi, and David Wajc

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

Abstract
The maximum matching problem in dynamic graphs subject to edge updates (insertions and deletions) has received much attention over the last few years; a multitude of approximation/time tradeoffs were obtained, improving upon the folklore algorithm, which maintains a maximal (and hence 2-approximate) matching in O(n) worst-case update time in n-node graphs. We present the first deterministic algorithm which outperforms the folklore algorithm in terms of both approximation ratio and worst-case update time. Specifically, we give a (2-Ω(1))-approximate algorithm with O(m^{3/8}) = O(n^{3/4}) worst-case update time in n-node, m-edge graphs. For sufficiently small constant ε > 0, no deterministic (2+ε)-approximate algorithm with worst-case update time O(n^{0.99}) was known. Our second result is the first deterministic (2+ε)-approximate weighted matching algorithm with O_ε(1)⋅ O(∜{m}) = O_ε(1)⋅ O(√n) worst-case update time. Neither of our results were previously known to be achievable by a randomized algorithm against an adaptive adversary. Our main technical contributions are threefold: first, we characterize the tight cases for kernels, which are the well-studied matching sparsifiers underlying much of the (2+ε)-approximate dynamic matching literature. This characterization, together with multiple ideas - old and new - underlies our result for breaking the approximation barrier of 2. Our second technical contribution is the first example of a dynamic matching algorithm whose running time is improved due to improving the recourse of other dynamic matching algorithms. Finally, we show how to use dynamic bipartite matching algorithms as black-box subroutines for dynamic matching in general graphs without incurring the natural 3/2 factor in the approximation ratio which such approaches naturally incur (reminiscent of the integrality gap of the fractional matching polytope in general graphs).
Cite as

Mohammad Roghani, Amin Saberi, and David Wajc. Beating the Folklore Algorithm for Dynamic Matching. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 111:1-111:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{roghani_et_al:LIPIcs.ITCS.2022.111,
  author =	{Roghani, Mohammad and Saberi, Amin and Wajc, David},
  title =	{{Beating the Folklore Algorithm for Dynamic Matching}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{111:1--111:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.111},
  URN =		{urn:nbn:de:0030-drops-157077},
  doi =		{10.4230/LIPIcs.ITCS.2022.111},
  annote =	{Keywords: dynamic matching, dynamic graph algorithms, sublinear algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.23
On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications

Authors: Sayan Bandyapadhyay, Fedor V. Fomin, and Kirill Simonov

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

Abstract
Fair clustering is a variant of constrained clustering where the goal is to partition a set of colored points. The fraction of points of each color in every cluster should be more or less equal to the fraction of points of this color in the dataset. This variant was recently introduced by Chierichetti et al. [NeurIPS 2017] and became widely popular. This paper proposes a new construction of coresets for fair k-means and k-median clustering for Euclidean and general metrics based on random sampling. For the Euclidean space ℝ^d, we provide the first coresets whose size does not depend exponentially on the dimension d. The question of whether such constructions exist was asked by Schmidt, Schwiegelshohn, and Sohler [WAOA 2019] and Huang, Jiang, and Vishnoi [NeurIPS 2019]. For general metric, our construction provides the first coreset for fair k-means and k-median. New coresets appear to be a handy tool for designing better approximation and streaming algorithms for fair and other constrained clustering variants. In particular, we obtain - the first fixed-parameter tractable (FPT) PTAS for fair k-means and k-median clustering in ℝ^d. The near-linear time of our PTAS improves over the previous scheme of Böhm, Fazzone, Leonardi, and Schwiegelshohn [ArXiv 2020] with running time n^{poly(k/ε)}; - FPT "true" constant-approximation for metric fair clustering. All previous algorithms for fair k-means and k-median in general metric are bicriteria and violate the fairness constraints; - FPT 3-approximation for lower-bounded k-median improving the best-known 3.736 factor of Bera, Chakrabarty, and Negahbani [ArXiv 2019]; - the first FPT constant-approximations for metric chromatic clustering and 𝓁-Diversity clustering; - near linear-time (in n) PTAS for capacitated and lower-bounded clustering improving over PTAS of Bhattacharya, Jaiswal, and Kumar [TOCS 2018] with super-quadratic running time; - a streaming (1+ε)-approximation for fair k-means and k-median of space complexity polynomial in k, d, ε and log{n} (the previous algorithms have exponential space complexity on either d or k).
Cite as

Sayan Bandyapadhyay, Fedor V. Fomin, and Kirill Simonov. On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bandyapadhyay_et_al:LIPIcs.ICALP.2021.23,
  author =	{Bandyapadhyay, Sayan and Fomin, Fedor V. and Simonov, Kirill},
  title =	{{On Coresets for Fair Clustering in Metric and Euclidean Spaces and Their Applications}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.23},
  URN =		{urn:nbn:de:0030-drops-140923},
  doi =		{10.4230/LIPIcs.ICALP.2021.23},
  annote =	{Keywords: fair clustering, coresets, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.27
Deterministic Rounding of Dynamic Fractional Matchings

Authors: Sayan Bhattacharya and Peter Kiss

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

Abstract
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algorithm for maintaining a (2-δ)-approximate maximum matching in a fully dynamic bipartite graph, in arbitrarily small polynomial update time. (2) The first deterministic algorithm for maintaining a (1+δ)-approximate maximum matching in a decremental bipartite graph, in polylogarithmic update time. (3) The first deterministic algorithm for maintaining a (2+δ)-approximate maximum matching in a fully dynamic general graph, in small polylogarithmic (specifically, O(log⁴ n)) update time. These results are respectively obtained by applying our framework on top of the fractional matching algorithms of Bhattacharya et al. [STOC'16], Bernstein et al. [FOCS'20], and Bhattacharya and Kulkarni [SODA'19]. Previously, there were two known general-purpose rounding schemes for dynamic fractional matchings. Both these schemes, by Arar et al. [ICALP'18] and Wajc [STOC'20], were randomized. Our rounding scheme works by maintaining a good matching-sparsifier with bounded arboricity, and then applying the algorithm of Peleg and Solomon [SODA'16] to maintain a near-optimal matching in this low arboricity graph. To the best of our knowledge, this is the first dynamic matching algorithm that works on general graphs by using an algorithm for low-arboricity graphs as a black-box subroutine. This feature of our rounding scheme might be of independent interest.
Cite as

Sayan Bhattacharya and Peter Kiss. Deterministic Rounding of Dynamic Fractional Matchings. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bhattacharya_et_al:LIPIcs.ICALP.2021.27,
  author =	{Bhattacharya, Sayan and Kiss, Peter},
  title =	{{Deterministic Rounding of Dynamic Fractional Matchings}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.27},
  URN =		{urn:nbn:de:0030-drops-140960},
  doi =		{10.4230/LIPIcs.ICALP.2021.27},
  annote =	{Keywords: Matching, Dynamic Algorithms, Data Structures}
}
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