10 Search Results for "Gamlath, Buddhima"

Document
DOI: 10.4230/LIPIcs.ISAAC.2025.13
Optimal Online Bipartite Matching in Degree-2 Graphs

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.
Cite as

Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
  author =	{Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
  title =	{{Optimal Online Bipartite Matching in Degree-2 Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.13},
  URN =		{urn:nbn:de:0030-drops-249216},
  doi =		{10.4230/LIPIcs.ISAAC.2025.13},
  annote =	{Keywords: Online Algorithm, Bipartite matching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.17
Weighted Matching in a Poly-Streaming Model

Authors: Ahammed Ullah, S M Ferdous, and Alex Pothen

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We introduce the poly-streaming model, a generalization of streaming models of computation in which k processors process k data streams containing a total of N items. The algorithm is allowed 𝒪(f(k)⋅M₁) space, where M₁ is either o (N) or the space bound for a sequential streaming algorithm. Processors may communicate as needed. Algorithms are assessed by the number of passes, per-item processing time, total runtime, space usage, communication cost, and solution quality. We design a single-pass algorithm in this model for approximating the maximum weight matching (MWM) problem. Given k edge streams and a parameter ε > 0, the algorithm computes a (2+ε)-approximate MWM. We analyze its performance in a shared-memory parallel setting: for any constant ε > 0, it runs in time 𝒪̃(L_{max}+n), where n is the number of vertices and L_{max} is the maximum stream length. It supports 𝒪(1) per-edge processing time using 𝒪̃(k⋅n) space. We further generalize the design to hierarchical architectures, in which k processors are partitioned into r groups, each with its own shared local memory. The total intergroup communication is 𝒪̃(r⋅n) bits, while all other performance guarantees are preserved. We evaluate the algorithm on a shared-memory system using graphs with trillions of edges. It achieves substantial speedups as k increases and produces matchings with weights significantly exceeding the theoretical guarantee. On our largest test graph, it reduces runtime by nearly two orders of magnitude and memory usage by five orders of magnitude compared to an offline algorithm.
Cite as

Ahammed Ullah, S M Ferdous, and Alex Pothen. Weighted Matching in a Poly-Streaming Model. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ullah_et_al:LIPIcs.ESA.2025.17,
  author =	{Ullah, Ahammed and Ferdous, S M and Pothen, Alex},
  title =	{{Weighted Matching in a Poly-Streaming Model}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.17},
  URN =		{urn:nbn:de:0030-drops-244858},
  doi =		{10.4230/LIPIcs.ESA.2025.17},
  annote =	{Keywords: Streaming Algorithms, Matchings, Graphs, Parallel Algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.50
Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries

Authors: Tatsuya Terao

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
In the matroid intersection problem, we are given two matroids ℳ₁ = (V, ℐ₁) and ℳ₂ = (V, ℐ₂) defined on the same ground set V of n elements, and the objective is to find a common independent set S ∈ ℐ₁ ∩ ℐ₂ of largest possible cardinality, denoted by r. In this paper, we consider a deterministic matroid intersection algorithm with only a nearly linear number of independence oracle queries. Our contribution is to present a deterministic O(n/(ε) + r log r)-independence-query (2/3-ε)-approximation algorithm for any ε > 0. Our idea is very simple: we apply a recent Õ(n √r/ε)-independence-query (1 - ε)-approximation algorithm of Blikstad [ICALP 2021], but terminate it before completion. Moreover, we also present a semi-streaming algorithm for (2/3 -ε)-approximation of matroid intersection in O(1/ε) passes.
Cite as

Tatsuya Terao. Deterministic (2/3 - ε)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 50:1-50:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{terao:LIPIcs.WADS.2025.50,
  author =	{Terao, Tatsuya},
  title =	{{Deterministic (2/3 - \epsilon)-Approximation of Matroid Intersection Using Nearly-Linear Independence-Oracle Queries}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{50:1--50:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.50},
  URN =		{urn:nbn:de:0030-drops-242812},
  doi =		{10.4230/LIPIcs.WADS.2025.50},
  annote =	{Keywords: Matroid intersection, approximation algorithm, streaming algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.58
A New Impossibility Result for Online Bipartite Matching Problems

Authors: Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi [Manshadi et al., 2011] in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio. In this paper we show that no algorithm can achieve a competitive ratio better than 1- e/(e^e) = 0.82062…, improving upon the 0.823 upper bound presented in [Manshadi et al., 2011]. Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1 - 1/e, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.
Cite as

Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani. A New Impossibility Result for Online Bipartite Matching Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chierichetti_et_al:LIPIcs.ICALP.2025.58,
  author =	{Chierichetti, Flavio and Giacchini, Mirko and Panconesi, Alessandro and Vattani, Andrea},
  title =	{{A New Impossibility Result for Online Bipartite Matching Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{58:1--58:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.58},
  URN =		{urn:nbn:de:0030-drops-234354},
  doi =		{10.4230/LIPIcs.ICALP.2025.58},
  annote =	{Keywords: Bipartite Matching, Random Graphs, Competitive Ratio}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.119
Faster Semi-Streaming Matchings via Alternating Trees

Authors: Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We design a deterministic algorithm for the (1+ε)-approximate maximum matching problem. Our primary result demonstrates that this problem can be solved in O(ε^{-6}) semi-streaming passes, improving upon the O(ε^{-19}) pass-complexity algorithm by [Fischer, Mitrović, and Uitto, STOC'22]. This contributes substantially toward resolving Open question 2 from [Assadi, SOSA'24]. Leveraging the framework introduced in [FMU'22], our algorithm achieves an analogous round complexity speed-up for computing a (1+ε)-approximate maximum matching in both the Massively Parallel Computation (MPC) and CONGEST models. The data structures maintained by our algorithm are formulated using blossom notation and represented through alternating trees. This approach enables a simplified correctness analysis by treating specific components as if operating on bipartite graphs, effectively circumventing certain technical intricacies present in prior work.
Cite as

Slobodan Mitrović, Anish Mukherjee, Piotr Sankowski, and Wen-Horng Sheu. Faster Semi-Streaming Matchings via Alternating Trees. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 119:1-119:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mitrovic_et_al:LIPIcs.ICALP.2025.119,
  author =	{Mitrovi\'{c}, Slobodan and Mukherjee, Anish and Sankowski, Piotr and Sheu, Wen-Horng},
  title =	{{Faster Semi-Streaming Matchings via Alternating Trees}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{119:1--119:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.119},
  URN =		{urn:nbn:de:0030-drops-234965},
  doi =		{10.4230/LIPIcs.ICALP.2025.119},
  annote =	{Keywords: streaming algorithms, approximation algorithms, maximum matching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.67
Query Efficient Weighted Stochastic Matching

Authors: Mahsa Derakhshan and Mohammad Saneian

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
In this paper, we study the weighted stochastic matching problem. Let G = (V, E) be a given edge-weighted graph, and let its realization 𝒢 be a random subgraph of G that includes each edge e ∈ E independently with a known probability p_e. The goal in this problem is to pick a sparse subgraph Q of G without prior knowledge of 𝒢, such that the maximum weight matching among the realized edges of Q (i.e., the subgraph Q ∩ 𝒢) in expectation approximates the maximum weight matching of the entire realization 𝒢. It is established by previous work that attaining any constant approximation ratio for this problem requires selecting a subgraph of max-degree Ω(1/p), where p = min_{e ∈ E} p_e. On the positive side, there exists a (1-ε)-approximation algorithm by Behnezhad and Derakhshan [FOCS'20], albeit at the cost of a max-degree having exponential dependence on 1/p. Within the O(1/p) query regime, however, the best-known algorithm achieves a 0.536 approximation ratio due to Dughmi, Kalayci, and Patel [ICALP'23], improving over the 0.501 approximation algorithm by Behnezhad, Farhadi, Hajiaghayi, and Reyhani [SODA'19]. In this work, we present a 0.68-approximation algorithm with the asymptotically optimal O(1/p) queries per vertex. Our result not only substantially improves the approximation ratio for weighted graphs, but also breaks the well-known 2/3 barrier with the optimal number of queries - even for unweighted graphs. Our analysis involves reducing the problem to designing a randomized matching algorithm on a given stochastic graph with some variance-bounding properties. To achieve these properties, we leverage a randomized algorithm by MacRury and Ma [STOC'24] for a variant of online stochastic matching.
Cite as

Mahsa Derakhshan and Mohammad Saneian. Query Efficient Weighted Stochastic Matching. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{derakhshan_et_al:LIPIcs.ICALP.2025.67,
  author =	{Derakhshan, Mahsa and Saneian, Mohammad},
  title =	{{Query Efficient Weighted Stochastic Matching}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{67:1--67:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.67},
  URN =		{urn:nbn:de:0030-drops-234445},
  doi =		{10.4230/LIPIcs.ICALP.2025.67},
  annote =	{Keywords: Sublinear algorithms, Stochastic, Matching}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.9
Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model

Authors: Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We investigate semi-streaming algorithms for the Traveling Salesman Problem (TSP). Specifically, we focus on a variant known as the (1,2)-TSP, where the distances between any two vertices are either one or two. Our primary emphasis is on the closely related Maximum Path Cover Problem, which aims to find a collection of vertex-disjoint paths that covers the maximum number of edges in a graph. We propose an algorithm that, for any ε > 0, achieves a (2/3-ε)-approximation of the maximum path cover size for an n-vertex graph, using poly(1/ε) passes. This result improves upon the previous 1/2-approximation by Behnezhad et al. [Soheil Behnezhad et al., 2023] in the semi-streaming model. Building on this result, we design a semi-streaming algorithm that constructs a tour for an instance of (1,2)-TSP with an approximation factor of (4/3 + ε), improving upon the previous 3/2-approximation factor algorithm by Behnezhad et al. [Soheil Behnezhad et al., 2023]. Furthermore, we extend our approach to develop an approximation algorithm for the Maximum TSP (Max-TSP), where the goal is to find a Hamiltonian cycle with the maximum possible weight in a given weighted graph G. Our algorithm provides a (7/12 - ε)-approximation for Max-TSP in poly(1/(ε)) passes, improving on the previously known (1/2-ε)-approximation obtained via maximum weight matching in the semi-streaming model.
Cite as

Sharareh Alipour, Ermiya Farokhnejad, and Tobias Mömke. Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alipour_et_al:LIPIcs.STACS.2025.9,
  author =	{Alipour, Sharareh and Farokhnejad, Ermiya and M\"{o}mke, Tobias},
  title =	{{Improved Approximation Algorithms for (1,2)-TSP and Max-TSP Using Path Covers in the Semi-Streaming Model}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.9},
  URN =		{urn:nbn:de:0030-drops-228342},
  doi =		{10.4230/LIPIcs.STACS.2025.9},
  annote =	{Keywords: (1,2)-TSP, Max-TSP, Maximum Path Cover, Semi-Streaming Algorithms, Approximation Algorithms, Graph Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.43
Space Complexity of Minimum Cut Problems in Single-Pass Streams

Authors: Matthew Ding, Alexandro Garces, Jason Li, Honghao Lin, Jelani Nelson, Vihan Shah, and David P. Woodruff

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less well-studied. To this end, we show upper and lower bounds on minimum cut problems in insertion-only streams for a variety of settings, including for both randomized and deterministic algorithms, for both arbitrary and random order streams, and for both approximate and exact algorithms. One of our main results is an Õ(n/ε) space algorithm with fast update time for approximating a spectral cut query with high probability on a stream given in an arbitrary order. Our result breaks the Ω(n/ε²) space lower bound required of a sparsifier that approximates all cuts simultaneously. Using this result, we provide streaming algorithms with near optimal space of Õ(n/ε) for minimum cut and approximate all-pairs effective resistances, with matching space lower-bounds. The amortized update time of our algorithms is Õ(1), provided that the number of edges in the input graph is at least (n/ε²)^{1+o(1)}. We also give a generic way of incorporating sketching into a recursive contraction algorithm to improve the post-processing time of our algorithms. In addition to these results, we give a random-order streaming algorithm that computes the exact minimum cut on a simple, unweighted graph using Õ(n) space. Finally, we give an Ω(n/ε²) space lower bound for deterministic minimum cut algorithms which matches the best-known upper bound up to polylogarithmic factors.
Cite as

Matthew Ding, Alexandro Garces, Jason Li, Honghao Lin, Jelani Nelson, Vihan Shah, and David P. Woodruff. Space Complexity of Minimum Cut Problems in Single-Pass Streams. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 43:1-43:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ding_et_al:LIPIcs.ITCS.2025.43,
  author =	{Ding, Matthew and Garces, Alexandro and Li, Jason and Lin, Honghao and Nelson, Jelani and Shah, Vihan and Woodruff, David P.},
  title =	{{Space Complexity of Minimum Cut Problems in Single-Pass Streams}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{43:1--43:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.43},
  URN =		{urn:nbn:de:0030-drops-226714},
  doi =		{10.4230/LIPIcs.ITCS.2025.43},
  annote =	{Keywords: minimum cut, approximate, random order, lower bound}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.57
Approximating Star Cover Problems

Authors: Buddhima Gamlath and Vadim Grinberg

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
Given a metric space (F ∪ C, d), we consider star covers of C with balanced loads. A star is a pair (i, C_i) where i ∈ F and C_i ⊆ C, and the load of a star is ∑_{j ∈ C_i} d(i, j). In minimum load k-star cover problem (MLkSC), one tries to cover the set of clients C using k stars that minimize the maximum load of a star, and in minimum size star cover (MSSC) one aims to find the minimum number of stars of load at most T needed to cover C, where T is a given parameter. We obtain new bicriteria approximations for the two problems using novel rounding algorithms for their standard LP relaxations. For MLkSC, we find a star cover with (1+O(ε))k stars and O(1/ε²)OPT_MLk load where OPT_MLk is the optimum load. For MSSC, we find a star cover with O(1/ε²) OPT_MS stars of load at most (2 + O(ε)) T where OPT_MS is the optimal number of stars for the problem. Previously, non-trivial bicriteria approximations were known only when F = C.
Cite as

Buddhima Gamlath and Vadim Grinberg. Approximating Star Cover Problems. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gamlath_et_al:LIPIcs.APPROX/RANDOM.2020.57,
  author =	{Gamlath, Buddhima and Grinberg, Vadim},
  title =	{{Approximating Star Cover Problems}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{57:1--57:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.57},
  URN =		{urn:nbn:de:0030-drops-126609},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.57},
  annote =	{Keywords: star cover, approximation algorithms, lp rounding}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.57
Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering

Authors: Buddhima Gamlath, Sangxia Huang, and Ola Svensson

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We study k-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are sufficient to efficiently recover a clustering that, with probability at least (1 - delta), simultaneously has a cost of at most (1 + epsilon) times the optimal cost and an accuracy of at least (1 - epsilon)? We show how to achieve such a clustering on n points with O{((k^2 log n) * m{(Q, epsilon^4, delta / (k log n))})} oracle queries, when the k clusters can be learned with an epsilon' error and a failure probability delta' using m(Q, epsilon',delta') labeled samples in the supervised setting, where Q is the set of candidate cluster centers. We show that m(Q, epsilon', delta') is small both for k-means instances in Euclidean space and for those in finite metric spaces. We further show that, for the Euclidean k-means instances, we can avoid the dependency on n in the query complexity at the expense of an increased dependency on k: specifically, we give a slightly more involved algorithm that uses O{(k^4/(epsilon^2 delta) + (k^{9}/epsilon^4) log(1/delta) + k * m{({R}^r, epsilon^4/k, delta)})} oracle queries. We also show that the number of queries needed for (1 - epsilon)-accuracy in Euclidean k-means must linearly depend on the dimension of the underlying Euclidean space, and for finite metric space k-means, we show that it must at least be logarithmic in the number of candidate centers. This shows that our query complexities capture the right dependencies on the respective parameters.
Cite as

Buddhima Gamlath, Sangxia Huang, and Ola Svensson. Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 57:1-57:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{gamlath_et_al:LIPIcs.ICALP.2018.57,
  author =	{Gamlath, Buddhima and Huang, Sangxia and Svensson, Ola},
  title =	{{Semi-Supervised Algorithms for Approximately Optimal and Accurate Clustering}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{57:1--57:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.57},
  URN =		{urn:nbn:de:0030-drops-90612},
  doi =		{10.4230/LIPIcs.ICALP.2018.57},
  annote =	{Keywords: Clustering, Semi-supervised Learning, Approximation Algorithms, k-Means, k-Median}
}
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