Christian Engels

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Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of random metric instances for optimization problems obtained as follows: Every edge of a complete graph gets a weight drawn(More)
The traveling salesman problem (TSP) is one of the most important problems in combinatorial optimization: Given a complete graph with edge weights, the goal is to find a Hamiltonian cycle (also called a tour) of minimum weight. 2-opt is probably the most widely used local search heuristic for the TSP. It incrementally improves an initial tour by exchanging(More)
We construct a hitting set generator for sparse multivariate polynomials over the reals. The seed length of our generator is O(log2(mn/ )) where m is the number of monomials, n is number of variables, and 1− is the hitting probability. The generator can be evaluated in time polynomial in logm, n, and log 1/ . This is the first hitting set generator whose(More)
In this paper, we will show dichotomy theorems for the computation of polynomials corresponding to evaluation of graph homomorphisms in Valiant’s model. We are given a fixed graph H and want to find all graphs, from some graph class, homomorphic to this H. These graphs will be encoded by a family of polynomials. We give dichotomies for the polynomials for(More)
The power symmetric polynomial on n variables of degree d is defined as pd(x1, . . . , xn) = x d 1 + · · · + xn. We study polynomials that are expressible as a sum of powers of homogenous linear projections of power symmetric polynomials. These form a subclass of polynomials computed by depth five circuits with summation and powering gates (i.e., ∑∧∑∧∑(More)