9 Search Results for "Chung, Hao"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.2
Online Time-Windows TSP with Predictions

Authors: Shuchi Chawla and Dimitris Christou

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
In the Time-Windows TSP (TW-TSP) we are given requests at different locations on a network; each request is endowed with a reward and an interval of time; the goal is to find a tour that visits as much reward as possible during the corresponding time window. For the online version of this problem, where each request is revealed at the start of its time window, no finite competitive ratio can be obtained. We consider a version of the problem where the algorithm is presented with predictions of where and when the online requests will appear, without any knowledge of the quality of this side information. Vehicle routing problems such as the TW-TSP can be very sensitive to errors or changes in the input due to the hard time-window constraints, and it is unclear whether imperfect predictions can be used to obtain a finite competitive ratio. We show that good performance can be achieved by explicitly building slack into the solution. Our main result is an online algorithm that achieves a competitive ratio logarithmic in the diameter of the underlying network, matching the performance of the best offline algorithm to within factors that depend on the quality of the provided predictions. The competitive ratio degrades smoothly as a function of the quality and we show that this dependence is tight within constant factors.
Cite as

Shuchi Chawla and Dimitris Christou. Online Time-Windows TSP with Predictions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chawla_et_al:LIPIcs.APPROX/RANDOM.2024.2,
  author =	{Chawla, Shuchi and Christou, Dimitris},
  title =	{{Online Time-Windows TSP with Predictions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{2:1--2:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  URN =		{urn:nbn:de:0030-drops-209954},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.2},
  annote =	{Keywords: Travelling Salesman Problem, Predictions, Learning-Augmented Algorithms, Approximation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.16
Weighted Matching in the Random-Order Streaming and Robust Communication Models

Authors: Diba Hashemi and Weronika Wrzos-Kaminska

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the maximum weight matching problem in the random-order semi-streaming model and in the robust communication model. Unlike many other sublinear models, in these two frameworks, there is a large gap between the guarantees of the best known algorithms for the unweighted and weighted versions of the problem. In the random-order semi-streaming setting, the edges of an n-vertex graph arrive in a stream in a random order. The goal is to compute an approximate maximum weight matching with a single pass over the stream using O(npolylog n) space. Our main result is a (2/3-ε)-approximation algorithm for maximum weight matching in random-order streams, using space O(n log n log R), where R is the ratio between the heaviest and the lightest edge in the graph. Our result nearly matches the best known unweighted (2/3+ε₀)-approximation (where ε₀ ∼ 10^{-14} is a small constant) achieved by Assadi and Behnezhad [Assadi and Behnezhad, 2021], and significantly improves upon previous weighted results. Our techniques also extend to the related robust communication model, in which the edges of a graph are partitioned randomly between Alice and Bob. Alice sends a single message of size O(npolylog n) to Bob, who must compute an approximate maximum weight matching. We achieve a (5/6-ε)-approximation using O(n log n log R) words of communication, matching the results of Azarmehr and Behnezhad [Azarmehr and Behnezhad, 2023] for unweighted graphs.
Cite as

Diba Hashemi and Weronika Wrzos-Kaminska. Weighted Matching in the Random-Order Streaming and Robust Communication Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hashemi_et_al:LIPIcs.APPROX/RANDOM.2024.16,
  author =	{Hashemi, Diba and Wrzos-Kaminska, Weronika},
  title =	{{Weighted Matching in the Random-Order Streaming and Robust Communication Models}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.16},
  URN =		{urn:nbn:de:0030-drops-210097},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.16},
  annote =	{Keywords: Maximum Weight Matching, Streaming, Random-Order Streaming, Robust Communication Complexity}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.39
Formalizing, Mechanizing, and Verifying Class-Based Refinement Types

Authors: Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Refinement types have been extensively used in class-based languages to specify and verify fine-grained logical specifications. Despite the advances in practical aspects such as applicability and usability, two fundamental issues persist. First, the soundness of existing class-based refinement type systems is inadequately explored, casting doubts on their reliability. Second, the expressiveness of existing systems is limited, restricting the depiction of semantic properties related to object-oriented constructs. This work tackles these issues through a systematic framework. We formalize a declarative class-based refinement type calculus (named RFJ), that is expressive and concise. We rigorously develop the soundness meta-theory of this calculus, followed by its mechanization in Coq. Finally, to ensure the calculus’s verifiability, we propose an algorithmic verification approach based on a fragment of first-order logic (named LFJ), and implement this approach as a type checker.
Cite as

Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao. Formalizing, Mechanizing, and Verifying Class-Based Refinement Types. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 39:1-39:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sun_et_al:LIPIcs.ECOOP.2024.39,
  author =	{Sun, Ke and Wang, Di and Chen, Sheng and Wang, Meng and Hao, Dan},
  title =	{{Formalizing, Mechanizing, and Verifying Class-Based Refinement Types}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{39:1--39:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.39},
  URN =		{urn:nbn:de:0030-drops-208881},
  doi =		{10.4230/LIPIcs.ECOOP.2024.39},
  annote =	{Keywords: Refinement Types, Program Verification, Object-oriented Programming}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.27
Improved Cut Strategy for Tensor Network Contraction Orders

Authors: Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
In the field of quantum computing, simulating quantum systems on classical computers is crucial. Tensor networks are fundamental in simulating quantum systems. A tensor network is a collection of tensors, that need to be contracted into a result tensor. Tensor contraction is a generalization of matrix multiplication to higher order tensors. The contractions can be performed in different orders, and the order has a significant impact on the number of floating point operations (flops) needed to get the result tensor. It is known that finding an optimal contraction order is NP-hard. The current state-of-the-art approach for finding efficient contraction orders is to combinine graph partitioning with a greedy strategy. Although heavily used in practice, the current approach ignores so-called free indices, chooses node weights without regarding previous computations, and requires numerous hyperparameters that need to be tuned at runtime. In this paper, we address these shortcomings by developing a novel graph cut strategy. The proposed modifications yield contraction orders that significantly reduce the number of flops in the tensor contractions compared to the current state of the art. Moreover, by removing the need for hyperparameter tuning at runtime, our approach converges to an efficient solution faster, which reduces the required optimization time by at least an order of magnitude.
Cite as

Christoph Staudt, Mark Blacher, Julien Klaus, Farin Lippmann, and Joachim Giesen. Improved Cut Strategy for Tensor Network Contraction Orders. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 27:1-27:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{staudt_et_al:LIPIcs.SEA.2024.27,
  author =	{Staudt, Christoph and Blacher, Mark and Klaus, Julien and Lippmann, Farin and Giesen, Joachim},
  title =	{{Improved Cut Strategy for Tensor Network Contraction Orders}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{27:1--27:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.27},
  URN =		{urn:nbn:de:0030-drops-203924},
  doi =		{10.4230/LIPIcs.SEA.2024.27},
  annote =	{Keywords: tensor network, contraction order, graph partitioniong, quantum simulation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.13
Learning Low-Degree Quantum Objects

Authors: Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos

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

Abstract
We consider the problem of learning low-degree quantum objects up to ε-error in 𝓁₂-distance. We show the following results: (i) unknown n-qubit degree-d (in the Pauli basis) quantum channels and unitaries can be learned using O(1/ε^d) queries (which is independent of n), (ii) polynomials p:{-1,1}ⁿ → [-1,1] arising from d-query quantum algorithms can be learned from O((1/ε)^d ⋅ log n) many random examples (x,p(x)) (which implies learnability even for d = O(log n)), and (iii) degree-d polynomials p:{-1,1}ⁿ → [-1,1] can be learned through O(1/ε^d) queries to a quantum unitary U_p that block-encodes p. Our main technical contributions are new Bohnenblust-Hille inequalities for quantum channels and completely bounded polynomials.
Cite as

Srinivasan Arunachalam, Arkopal Dutt, Francisco Escudero Gutiérrez, and Carlos Palazuelos. Learning Low-Degree Quantum Objects. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{arunachalam_et_al:LIPIcs.ICALP.2024.13,
  author =	{Arunachalam, Srinivasan and Dutt, Arkopal and Escudero Guti\'{e}rrez, Francisco and Palazuelos, Carlos},
  title =	{{Learning Low-Degree Quantum Objects}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{13:1--13:19},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-201563},
  doi =		{10.4230/LIPIcs.ICALP.2024.13},
  annote =	{Keywords: Tomography}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.122
An Improved Integrality Gap for Disjoint Cycles in Planar Graphs

Authors: Niklas Schlomberg

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

Abstract
We present a new greedy rounding algorithm for the Cycle Packing Problem for uncrossable cycle families in planar graphs. This improves the best-known upper bound for the integrality gap of the natural packing LP to a constant slightly less than 3.5. Furthermore, the analysis works for both edge- and vertex-disjoint packing. The previously best-known constants were 4 for edge-disjoint and 5 for vertex-disjoint cycle packing. This result also immediately yields an improved Erdős-Pósa ratio: for any uncrossable cycle family in a planar graph, the minimum number of vertices (edges) needed to hit all cycles in the family is less than 8.38 times the maximum number of vertex-disjoint (edge-disjoint, respectively) cycles in the family. Some uncrossable cycle families of interest to which the result can be applied are the family of all cycles in a directed or undirected graph, in undirected graphs also the family of all odd cycles and the family of all cycles containing exactly one edge from a specified set of demand edges. The last example is an equivalent formulation of the fully planar Disjoint Paths Problem. Here the Erdős-Pósa ratio translates to a ratio between integral multi-commodity flows and minimum cuts.
Cite as

Niklas Schlomberg. An Improved Integrality Gap for Disjoint Cycles in Planar Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 122:1-122:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{schlomberg:LIPIcs.ICALP.2024.122,
  author =	{Schlomberg, Niklas},
  title =	{{An Improved Integrality Gap for Disjoint Cycles in Planar Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{122:1--122:15},
  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.2024.122},
  URN =		{urn:nbn:de:0030-drops-202651},
  doi =		{10.4230/LIPIcs.ICALP.2024.122},
  annote =	{Keywords: Cycle packing, planar graphs, disjoint paths}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.98
Maximizing Miner Revenue in Transaction Fee Mechanism Design

Authors: Ke Wu, Elaine Shi, and Hao Chung

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Transaction fee mechanism design is a new decentralized mechanism design problem where users bid for space on the blockchain. Several recent works showed that the transaction fee mechanism design fundamentally departs from classical mechanism design. They then systematically explored the mathematical landscape of this new decentralized mechanism design problem in two settings: in the plain setting where no cryptography is employed, and in a cryptography-assisted setting where the rules of the mechanism are enforced by a multi-party computation protocol. Unfortunately, in both settings, prior works showed that if we want the mechanism to incentivize honest behavior for both users as well as miners (possibly colluding with users), then the miner revenue has to be zero. Although adopting a relaxed, approximate notion of incentive compatibility gets around this zero miner-revenue limitation, the scaling of the miner revenue is nonetheless poor. In this paper, we show that if we make a mild reasonable-world assumption that there are sufficiently many honest users, we can circumvent the known limitations on miner revenue, and design auctions that generate asymptotically optimal miner revenue. We also systematically explore the mathematical landscape of transaction fee mechanism design under the new reasonable-world assumptions, and demonstrate how such assumptions can alter the feasibility and infeasibility landscape.
Cite as

Ke Wu, Elaine Shi, and Hao Chung. Maximizing Miner Revenue in Transaction Fee Mechanism Design. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 98:1-98:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wu_et_al:LIPIcs.ITCS.2024.98,
  author =	{Wu, Ke and Shi, Elaine and Chung, Hao},
  title =	{{Maximizing Miner Revenue in Transaction Fee Mechanism Design}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{98:1--98:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.98},
  URN =		{urn:nbn:de:0030-drops-196266},
  doi =		{10.4230/LIPIcs.ITCS.2024.98},
  annote =	{Keywords: Blockchain, Mechanism Design, Transaction Fee}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.97
What Can Cryptography Do for Decentralized Mechanism Design?

Authors: Elaine Shi, Hao Chung, and Ke Wu

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Recent works of Roughgarden (EC'21) and Chung and Shi (SODA'23) initiate the study of a new decentralized mechanism design problem called transaction fee mechanism design (TFM). Unlike the classical mechanism design literature, in the decentralized environment, even the auctioneer (i.e., the miner) can be a strategic player, and it can even collude with a subset of the users facilitated by binding side contracts. Chung and Shi showed two main impossibility results that rule out the existence of a dream TFM. First, any TFM that provides incentive compatibility for individual users and miner-user coalitions must always have zero miner revenue, no matter whether the block size is finite or infinite. Second, assuming finite block size, no non-trivial TFM can simultaneously provide incentive compatibility for any individual user and for any miner-user coalition. In this work, we explore what new models and meaningful relaxations can allow us to circumvent the impossibility results of Chung and Shi. Besides today’s model that does not employ cryptography, we introduce a new MPC-assisted model where the TFM is implemented by a joint multi-party computation (MPC) protocol among the miners. We prove several feasibility and infeasibility results for achieving strict and approximate incentive compatibility, respectively, in the plain model as well as the MPC-assisted model. We show that while cryptography is not a panacea, it indeed allows us to overcome some impossibility results pertaining to the plain model, leading to non-trivial mechanisms with useful guarantees that are otherwise impossible in the plain model. Our work is also the first to characterize the mathematical landscape of transaction fee mechanism design under approximate incentive compatibility, as well as in a cryptography-assisted model.
Cite as

Elaine Shi, Hao Chung, and Ke Wu. What Can Cryptography Do for Decentralized Mechanism Design?. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 97:1-97:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shi_et_al:LIPIcs.ITCS.2023.97,
  author =	{Shi, Elaine and Chung, Hao and Wu, Ke},
  title =	{{What Can Cryptography Do for Decentralized Mechanism Design?}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{97:1--97:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.97},
  URN =		{urn:nbn:de:0030-drops-176005},
  doi =		{10.4230/LIPIcs.ITCS.2023.97},
  annote =	{Keywords: Transaction Fee Mechanism Design}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.27
An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity

Authors: Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane

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

Abstract
This study considers the soft capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing vertex-weighted graph G=(V,E), which allows edge insertions and edge deletions, the goal is to design a data structure that maintains an approximate minimum vertex cover while satisfying the capacity constraint of each vertex. That is, when picking a copy of a vertex v in the cover, the number of v's incident edges covered by the copy is up to a given capacity of v. We extend Bhattacharya et al.'s work [SODA'15 and ICALP'15] to obtain a deterministic primal-dual algorithm for maintaining a constant-factor approximate minimum capacitated vertex cover with O(log n / epsilon) amortized update time, where n is the number of vertices in the graph. The algorithm can be extended to (1) a more general model in which each edge is associated with a non-uniform and unsplittable demand, and (2) the more general capacitated set cover problem.
Cite as

Hao-Ting Wei, Wing-Kai Hon, Paul Horn, Chung-Shou Liao, and Kunihiko Sadakane. An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 27:1-27:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{wei_et_al:LIPIcs.APPROX-RANDOM.2018.27,
  author =	{Wei, Hao-Ting and Hon, Wing-Kai and Horn, Paul and Liao, Chung-Shou and Sadakane, Kunihiko},
  title =	{{An O(1)-Approximation Algorithm for Dynamic Weighted Vertex Cover with Soft Capacity}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{27:1--27:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  URN =		{urn:nbn:de:0030-drops-94312},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.27},
  annote =	{Keywords: approximation algorithm, dynamic algorithm, primal-dual, vertex cover}
}
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