arXiv subjects

Yinyu Ye

Publications and source records attributed to Yinyu Ye.

148 records · Page 9Linked to original sources

arXiv2008

Stochastic Combinatorial Optimization under Probabilistic Constraints

In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center problem and the set cover problem, with uncertainty characterized by a probability distribution over set of points or elements to be covered. We consider these problems under adaptive and non-adaptive settings, and present efficient approximation algorithms for the case when underlying distribution is a product distribution. In contrast to the expected cost model prevalent in stochastic optimization literature, our problem definitions support restrictions on the probability distributions of the total costs, via incorporating constraints that bound the probability with which the incurred costs may exceed a given threshold.

cs.DS↗

arXiv2008

Parimutuel Betting on Permutations

We focus on a permutation betting market under parimutuel call auction model where traders bet on the final ranking of n candidates. We present a Proportional Betting mechanism for this market. Our mechanism allows the traders to bet on any subset of the n x n 'candidate-rank' pairs, and rewards them proportionally to the number of pairs that appear in the final outcome. We show that market organizer's decision problem for this mechanism can be formulated as a convex program of polynomial size. More importantly, the formulation yields a set of n x n unique marginal prices that are sufficient to price the bets in this mechanism, and are computable in polynomial-time. The marginal prices reflect the traders' beliefs about the marginal distributions over outcomes. We also propose techniques to compute the joint distribution over n! permutations from these marginal distributions. We show that using a maximum entropy criterion, we can obtain a concise parametric form (with only n x n parameters) for the joint distribution which is defined over an exponentially large state space. We then present an approximation algorithm for computing the parameters of this distribution. In fact, the algorithm addresses the generic problem of finding the maximum entropy distribution over permutations that has a given mean, and may be of independent interest.

cs.GT↗

arXiv2007

A polynomial time $\frac 3 2$ -approximation algorithm for the vertex cover problem on a class of graphs

We develop a polynomial time 3/2-approximation algorithm to solve the vertex cover problem on a class of graphs satisfying a property called ``active edge hypothesis''. The algorithm also guarantees an optimal solution on specially structured graphs. Further, we give an extended algorithm which guarantees a vertex cover $S_1$ on an arbitrary graph such that $|S_1|\leq {3/2} |S^*|+ξ$ where $S^*$ is an optimal vertex cover and $ξ$ is an error bound identified by the algorithm. We obtained $ξ= 0$ for all the test problems we have considered which include specially constructed instances that were expected to be hard. So far we could not construct a graph that gives $ξ\not= 0$.

cs.DS↗

arXiv2004

On Solving Fewnomials Over Intervals in Fewnomial Time

Let f be a degree D univariate polynomial with real coefficients and exactly m monomial terms. We show that in the special case m=3 we can approximate within eps all the roots of f in the interval [0,R] using just O(log(D)log(Dlog(R/eps))) arithmetic operations. In particular, we can count the number of roots in any bounded interval using just O(log^2 D) arithmetic operations. Our speed-ups are significant and near-optimal: The asymptotically sharpest previous complexity upper bounds for both problems were super-linear in D, while our algorithm has complexity close to the respective complexity lower bounds. We also discuss conditions under which our algorithms can be extended to general m, and a connection to a real analogue of Smale's 17th Problem.

math.NA↗