In optimization-based classification model selection, for example when using linear programming formulations, a standard approach is to penalize the L1 norm of some linear functional in order to select sparse models. Instead, we propose a novel integer linear program for sparse classifier selection, generalizing the minimum disagreement hyperplane problem whose complexity has been investigated ...

This paper presents a unified exact method for solving an extended model of the well-known Capacitated Vehicle Routing Problem (CVRP), called the Heterogenous Vehicle Routing Problem (HVRP), where a mixed fleet of vehicles having different capacities, routing and fixed costs is used to supply a set of customers. The HVRP model considered in this paper contains as special cases: the Single Depot...

We show that the standard linear programming relaxation for the tree augmentation problem in undirected graphs has an integrality ratio that approaches 3 2 . This refutes a conjecture of Cheriyan, Jordán, and Ravi (ESA 1999) that the integrality ratio is 4 3 .

With spectrum auctions as our prime motivation, in this paper we analyze combinatorial auctions where agents’ valuations exhibit complementarities. Assuming that the agents only value bundles of size at most k and also assuming that we can assess prices, we present a mechanism that is efficient, approximately envy-free, asymptotically strategy-proof and that has polynomial-time complexity. Modi...

Sufficient conditions characterizing the asymptotic stability and the hybrid L1/`1-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. The...

This paper discusses the problem of minimizing the cost of sheet metal punching when nesting (batching) orders. Although the problem is NP-complete, the solution to a linear programming relaxation yields an efficient heuristic. This paper analyzes the heuristic’s worst-case performance and discusses experimental results that demonstrate its ability to find good solutions across a range of cost ...

We consider ranking and clustering problems related to the aggregation of inconsistent information. Ailon, Charikar, and Newman [1] proposed randomized constant factor approximation algorithms for these problems. Together with Hegde and Jain, we recently proposed deterministic versions of some of these randomized algorithms [2]. With one exception, these algorithms required the solution of a li...

We present an approximation algorithm for the problem of finding a minimum-cost k-vertex connected spanning subgraph, assuming that the number of vertices is at least 6k. The approximation guarantee is six times the kth harmonic number (which is O(log k)), and this is also an upper bound on the integrality ratio for a standard linear programming relaxation.

In the Multiway Cut problem, we are given an undirected edge-weighted graph G = (V; E) with c e denoting the cost (weight) of edge e. We are also given a subset S of V , of size k, called the terminals. The objective is to nd a minimum cost set of edges whose removal ensures that the terminals are disconnected. In this paper, we study a bidirected linear programming relaxation of Multiway Cut. ...

Placing is a necessary skill for a personal robot to have in order to perform tasks such as arranging objects in a disorganized room. The object placements should not only be stable but also be in their semantically preferred placing areas and orientations. This is challenging because an environment can have a large variety of objects and placing areas that may not have been seen by the robot b...