Sara Ahmadian

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

Clustering is a classic topic in optimization with k-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for k-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of 9+≥ilon, a ratio that is known to be tight with respect to such methods.We overcome this barrier by presenting a new primal-dual approach that allows us to (1) exploit the geometric structure of k-means and (2) to satisfy the hard constraint that at most k clusters are selected without deteriorating the approximation guarantee. Our main result is a 6.357-approximation algorithm with respect to the standard LP relaxation. Our techniques are quite general and we also show improved guarantees for the general version of k-means where the underlying metric is not required to be Euclidean and for k-median in Euclidean metrics.

Improved Approximation Guarantees for Lower-Bounded Facility Location

We consider the lower-bounded facility location (LBFL) problem, which is a generalization of uncapacitated facility location (UFL), where each open facility is required to serve a certain minimum amount of demand. The current best approximation ratio for LBFL is 448 [17]. We substantially advance the state-of-the-art for LBFL by improving its approximation ratio from 448 [17] to 82.6.

Stabilizing Network Bargaining Games by Blocking Players

Cooperative matching games Shapley and Shubik and Network bargaining games Kleinberg and Tardos are games described by an undirected graph, where the vertices represent players. An important role in such games is played by stable graphs, that are graphs whose set of inessential vertices those that are exposed by at least one maximum matching are pairwise non adjacent. In fact, stable graphs characterize instances of such games that admit the existence of stable outcomes. In this paper, we focus on stabilizing instances of the above games by blocking as few players as possible. Formally, given a graph G we want to find a minimum cardinality set of vertices such that its removal from G yields a stable graph. We give a combinatorial polynomial-time algorithm for this problem, and develop approximation algorithms for some NP-hard weighted variants, where each vertex has an associated non-negative weight. Our approximation algorithms are LP-based, and we show that our analysis are almost tight by giving suitable lower bounds on the integrality gap of the used LP relaxations.

Approximation Algorithms for Clustering Problems with Lower Bounds and Outliers

We consider clustering problems with {\em non-uniform lower bounds and outliers}, and obtain the {\em first approximation guarantees} for these problems. We have a set

Stabilizing network bargaining games by blocking players

\F

Approximation Algorithms for Minimum-Load k -Facility Location

of facilities with lower bounds

Further Approximations for Demand Matching: Matroid Constraints and Minor-Closed Graphs.

\{L_i\}_{i\in\F}

Local-search based approximation algorithms for mobile facility location problems

and a set

Local-Search based Approximation Algorithms for Mobile Facility Location Problems: (Extended Abstract)

\D

Algorithms for Inverse Optimization Problems.

of clients located in a common metric space