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We consider the stochastic graph model where the location of each vertex is a random point in a given metric space. We study the problems of computing the expected lengths of the minimum spanning tree, the minimum perfect matching and the minimum cycle cover on such a stochastic graph and obtain an FPRAS (Fully Polynomial Randomized Approximation Scheme)… (More)

We revisit the pairwise kidney exchange problem established by Roth Sonmez and Unver [23]. Our goal, explained in terms of graph theory, is to find a maximum fractional matching on an undirected graph, that Lorenz-dominates any other fractional matching. The Lorenz-dominant fractional matching , which can be implemented as a lottery of integral match-ings,… (More)

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing ε-kernel coresets for uncertain points. We consider… (More)

We consider the <i>multi-shop ski rental</i> problem. This problem generalizes the classic ski rental problem to a multi-shop setting, in which each shop has different prices for renting and purchasing a pair of skis, and a <i>consumer</i> has to make decisions on when and where to buy. We are interested in the <i>optimal online (competitive-ratio… (More)

Markov Chain Monte Carlo (MCMC) method is a widely used algorithm design scheme with many applications. To make efficient use of this method, the key step is to prove that the Markov chain is rapid mixing. Canonical paths is one of the two main tools to prove rapid mixing. However, there are much fewer success examples comparing to coupling, the other main… (More)

- Hu Ding, Yu Liu, Lingxiao Huang, Jian Li
- 2016

Proof. It is easy to verify the communication cost, and thus we focus on the proof for the approximation ratio below. Similar to the proof of Theorem 1, the grid G is rewritten as {g 1 , · · · , g m } where m = (k + z) T , and for each g j , its corresponding intersection T l=1 M l i l is rewritten as S j. Meanwhile, we denote the index-set indicating the… (More)

Solving geometric optimization problems over uncertain data have become increasingly important in many applications and have attracted a lot of attentions in recent years. In this paper, we study two important geometric optimization problems, the k-center problem and the j-flat-center problem, over stochastic/uncertain data points in Euclidean spaces. For… (More)

- Hu Ding, Yu Liu, Lingxiao Huang, Jian Li
- ICML
- 2016

Distributed clustering has attracted significant attention in recent years. In this paper, we study the k-means problem in the distributed dimension setting, where the dimensions of the data are partitioned across multiple machines. We provide new approximation algorithms, which incur low communication costs and achieve constant approximation ratios. The… (More)