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Faster Matroid Intersection [article]

Deeparnab Chakrabarty, Yin Tat Lee, Aaron Sidford, Sahil Singla, and Sam Chiu-wai Wong
2019 arXiv   pre-print
The former result improves over the Õ(nr +n^3)-time algorithm by Lee, Sidford, and Wong.  ...  This improves upon the running time of O(nr^1.5) due to Cunningham in 1986 and Õ(n^2+n^3) due to Lee, Sidford, and Wong in 2015.  ...  This is due to the way the exchange graph is defined.  ... 
arXiv:1911.10765v1 fatcat:seloq5nt4jgdxibgeyuwo6y44y

Matroid Online Bipartite Matching and Vertex Cover [article]

Yajun Wang, Sam Chiu-wai Wong
2016 arXiv   pre-print
If we order L = {1, 2, ..., n} in such a way that y 1 ≤ y 2 ≤ ... ≤ y n .  ...  [Wang and Wong 2015] GreedyAllocation is 1 + α-competitive for (fractional) OBVC.  ... 
arXiv:1606.07863v1 fatcat:d6ip6sqzr5bcjooiawtisekk7i

Multiplicative Bidding in Online Advertising [article]

MohammadHossein Bateni, Jon Feldman, Vahab Mirrokni, Sam Chiu-wai Wong
2014 arXiv   pre-print
This assumption is reasonable in two ways.  ...  The name staircase originates from the fact that the rows and columns can be permuted in such a way that S indeed resembles a staircase (with possibly uneven step sizes). 1 δ 7 1 1 δ 7 1 δ 5 1 δ 3 1 δ  ... 
arXiv:1404.6727v1 fatcat:xl6cuhcwpzfwrbswqykkinfnmm

Subquadratic Submodular Function Minimization [article]

Deeparnab Chakrabarty and Yin Tat Lee and Aaron Sidford and Sam Chiu-wai Wong
2016 arXiv   pre-print
The current fastest algorithms [Lee, Sidford, Wong, FOCS 2015] run in O(n^2 nM·EO +n^3^O(1)nM) time and O(n^3^2n·EO +n^4^O(1)n) time respectively, where M is the largest absolute value of the function  ...  The only way to do this is via Carathedeory's Theorem which requires n vertices of B f , each of which requires n function evaluations.  ...  On the other hand, the best way we know of for certifying minimality takes Θ(n) subgradient oracle calls (or equivalently, vertices of the base polyhedron).  ... 
arXiv:1610.09800v1 fatcat:m52zt4wccvaibn5ku4vkuyvlzm

Online Vertex Cover and Matching: Beating the Greedy Algorithm [article]

Yajun Wang, Sam Chiu-wai Wong
2013 arXiv   pre-print
A natural way is to first express the optimal z in terms of f , and then use techniques from calculus of variation to compute the best f .  ...  Our strategy is to charge the potential increment to vertices of C * in such a way that each vertex of C * is charged at most 1 + α. Let v be the current online vertex.  ... 
arXiv:1305.1694v1 fatcat:f6wim7bkkng33g7o2xlc6wtdde

Tight Bounds for Approximate Carathéodory and Beyond [article]

Vahab Mirrokni, Renato Paes Leme, Adrian Vladu, Sam Chiu-wai Wong
2015 arXiv   pre-print
Along the way of establishing the upper bound, we develop a technique for minimizing norms over convex sets with complicated geometry; this is achieved by running Mirror Descent on a dual convex function  ...  One way to do that is using the Fenchel transform.  ...  Notice that the previous expression is a way to write any convex function as a maximum over linear functions in x parametrized by z.  ... 
arXiv:1512.08602v1 fatcat:mmivrsy3qrf7tmn3y4f2bp3asm

Network design for s-t effective resistance [article]

Pak Hay Chan, Lap Chi Lau, Aaron Schild, Sam Chiu-wai Wong, Hong Zhou
2019 arXiv   pre-print
We partition Y into groups Y 1 , . . . , Y b in a similar way. The following claim uses the small-set expansion property in G to show that there is no small dense subset in B. Lemma 5.11.  ...  constructed recursively as follows: • Base case: A single edge (s, t) • Compose step: If G 1 and G 2 are two series parallel graphs with source s i and target t i (i = 1, 2), then we can combine them in two ways  ... 
arXiv:1904.03219v1 fatcat:ms2lijqklfao5odfnnwnf24nei

Computing Walrasian equilibria: fast algorithms and structural properties

Renato Paes Leme, Sam Chiu-wai Wong
2018 Mathematical programming  
A key technical ingredient is to regularize a convex programming formulation of the problem in a way that subgradients are cheap to compute.  ...  Wong  ...  (PD) We want to specify the real-valued vector r in such a way that the optimal solution to this linear program is still the optimal solution to the original program, but also in a way that the optimal  ... 
doi:10.1007/s10107-018-1334-9 fatcat:fytimwept5dejbxc4i5qvvpk4e

Computing Walrasian Equilibria: Fast Algorithms and Structural Properties [article]

Renato Paes Leme, Sam Chiu-wai Wong
2016 arXiv   pre-print
A key technical ingredient is to regularize a convex programming formulation of the problem in a way that subgradients are cheap to compute.  ...  Theorem 3.6 (Lee, Sidford, Wong (Theorem 31 in [LSW15] )).  ...  In order to do so, we use a recent technique introduced by Lee, Sidford and Wong [LSW15] .  ... 
arXiv:1511.04032v2 fatcat:tharcfrx65b4xnr7y4nonpxuei

Truthful Online Scheduling of Cloud Workloads under Uncertainty [article]

Moshe Babaioff and Ronny Lempel and Brendan Lucier and Ishai Menache and Aleksandrs Slivkins and Sam Chiu-Wai Wong
2022 arXiv   pre-print
Given an instance I of MainProblem, we construct an instance of RelaxedProblem, denoted Relax(I), in a fairly natural way.  ...  The two problem variants carry over to RelaxedProblem in an obvious way. It is here where we use the assumption that ( , ) = .  ... 
arXiv:2203.01213v1 fatcat:nxen7wkd6rel7dnabp5c2uonfy

An Improved Cutting Plane Method for Convex Optimization, Convex-Concave Games and its Applications [article]

Haotian Jiang, Yin Tat Lee, Zhao Song, Sam Chiu-wai Wong
2020 arXiv   pre-print
. ∙ This improves upon Lee-Sidford-Wong's O( SO· n log (κ) + n^3 log^O(1) (κ)) time algorithm [Lee, Sidford and Wong, FOCS 2015] in terms of dependence on κ.  ...  [LW17] Renato Paes Leme and Sam Chiu-wai Wong. Computing walrasian equilibria: fast algorithms and structural properties.  ...  [LSW15] Yin Tat Lee, Aaron Sidford, and Sam Chiu-wai Wong. A faster cutting plane method and its implications for combinatorial and convex optimization.  ... 
arXiv:2004.04250v1 fatcat:imxhan7abfbbhbhygdkd6nbhsu

Tight Algorithms for Vertex Cover with Hard Capacities on Multigraphs and Hypergraphs [article]

Sam Chiu-wai Wong
2017 arXiv   pre-print
This improves over the previous 2.155 (for f=2) and 2f-approximation algorithms by Cheung, Goemans and Wong (CGW).  ...  We justify the capacity constraint in the next lemma, which goes hand-in-hand with the way LP3 is formulated. Lemma 10.  ...  In a way, their argument is a probabilistic proof that a 2-approximate solution exists for LP4, and our one-page analysis can be viewed as a simple deterministic proof of that claim.  ... 
arXiv:1606.07861v2 fatcat:l326we4sxbhmlofwdgsdzee7g4

A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization [article]

Yin Tat Lee, Aaron Sidford, Sam Chiu-wai Wong
2015 arXiv   pre-print
Therefore, it is an interesting question of whether there is a way of using an optimization oracle more directly.  ...  Our results demonstrate the power of cutting plane methods in theory and possibly pave the way for new cutting plane methods in practice.  ... 
arXiv:1508.04874v2 fatcat:74i57p5lardbnmstsdml66ovta

Improved Algorithms for Vertex Cover with Hard Capacities on Multigraphs and Hypergraphs [chapter]

Wang Chi Cheung, Michel X. Goemans, Sam Chiu-Wai Wong
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
Goemans † , Sam Chiu-wai Wong ‡ Abstract In this paper, we consider the minimum unweighted Vertex Cover problem with Hard Capacity constraints (VCHC) on multigraphs and hypergraphs.  ...  We then set up the covering LP in a similar way to the case of multigraphs, and round up its extreme point solution and include the correponding vertices into the solution. Organization.  ... 
doi:10.1137/1.9781611973402.124 dblp:conf/soda/CheungGW14 fatcat:atitlxvq2jcgnei4nnb3dsn6vy

Planting a Seed of Experience – Long Term Effects of a Co-curricular Ecogarden-Based Program in Higher Education in Hong Kong

Chi-Chiu Cheang, Wai-Ki Ng, Yuen-Sam Diana Wong, Wai-Chin Li, Kwok-Ho Tsoi
2021 Frontiers in Psychology  
I can have more ways to develop myself."  ...  I can have more ways to develop myself."  ...  Ken Tsan-Fung Wong for assistance in preparing the dataset and analysis. Special thanks go to Dr. Yeung-Chun Lee, Dr. Bill Chi-Ho Yeung, Dr. Brian Yu-Bon Man, Dr. James Chun-Wah Lam, Dr.  ... 
doi:10.3389/fpsyg.2020.583319 pmid:33519601 pmcid:PMC7843962 fatcat:nf6j6fh435fjneh64nujwdellq
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