There are several known results asserting that undirected graphs can be partitioned in a way that satisfies various imposed constrains on the degrees. The corresponding results for directed graphs, where degrees are replaced by outdegrees, often fail, and when they do hold, they are usually much harder, and lead to fascinating open problems. In this note we list three problems of this type, and...

The relay station simply rebroadcasts the signal it receives from the source, at exactly the instant that it receives it. The relay station therefore has no effect on the signal received by the observer, but it serves as a crutch for our thinking— it allows us to divide the problem into two parts, each already solved. Let ∆t denote the time interval between wave crests, with subscripts to indic...

In this work, we propose a novel K-ary splitting method for regression trees and incorporate it into the regression forest framework. Unlike standard binary splitting, where the splitting rule is selected from a predefined set of binary splitting rules via trial-and-error, the proposed K-ary splitting method first finds clusters of the training data which at least locally minimize the empirical...

Given positive integers a1, . . . , an, t, the fixed weight subset sum problem is to find a subset of the ai that sum to t, where the subset has a prescribed number of elements. It is this problem that underlies the security of modern knapsack cryptosystems, and solving the problem results directly in a message attack. We present new exponential algorithms that do not rely on lattices, and henc...

In this work, we propose a novel node splitting method for regression trees and incorporate it into the regression forest framework. Unlike traditional binary splitting, where the splitting rule is selected from a predefined set of binary splitting rules via trial-and-error, the proposed node splitting method first finds clusters of the training data which at least locally minimize the empirica...

We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the direct adaptation of the method to minimize the sum of a proper closed funct...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...

Abstract. We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-split...