We introduce three new cut tree structures of graphs G in which the vertex set of the tree is a partition of V (G) and contractions of tree vertices satisfy sparsification requirements that preserve various types of cuts. Recently, Kawarabayashi and Thorup [8] presented the first deterministic near-linear edge-connectivity recognition algorithm. A crucial step in this algorithm uses the existen...

In a recent paper [4] Balas, Ceria and Cornuejoels provided computational results that their Lift-and-Project method [3] successfully solved a series of pure and mixed 0-1 benchmark programs and performed on the average better than several commercial general mixed integer optimization packages existing at the time. The Lift-and-Project approach uses a linear programming formulation derived by i...

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...

We consider the question of determining the scaling of the n-dimensional unicast and the n×2n-dimensional multicast capacity regions of a wireless network with n nodes placed uniformly at random in a square region of area n and communicating over Gaussian fading channels. We identify this scaling of both the unicast and multicast capacity regions in terms of Θ(n), out of 2n total possible, cuts...

Many graph-based learning problems can be cast as finding a good set of vertices nearby a seed set, and a powerful methodology for these problems is based on maximum flows. We introduce and analyze a new method for locally-biased graphbased learning called SimpleLocal, which finds good conductance cuts near a set of seed vertices. An important feature of our algorithm is that it is strongly-loc...

We propose a heuristic search algorithm for finding optimal policies in a new class of sequential decision making problems. This class extends Markov decision processes by a limited type of hidden state, paying tribute to the fact that many robotic problems indeed possess hidden state. The proposed search algorithm exploits the problem formulation to devise a fast bound-searching algorithm, whi...

We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. We propose a Benders decomposition algorithm to find the optimal solution to the problem with a finite number of samples. We show that the submodularity...

We present a branch and cut algorithm that yields in nite time, a globally -optimal solution (with respect to feasibility and optimality) of the nonconvex quadratically constrained quadratic programming problem. The idea is to estimate all quadratic terms by successive linearizations within a branching tree using Reformulation-Linearization Techniques (RLT). To do so, four classes of linearizat...