Maximum ATSP with Weights Zero and One via Half-Edges

A 3/4-Approximation Algorithm for Maximum ATSP with Weights Zero and One

We present a polynomial time 3/4-approximation algorithm for the maximum asymmetric TSP with weights zero and one. As applications, we get a 5/4-approximation algorithm for the (minimum) asymmetric TSP with weights one and two and a 3/4-approximation algorithm for the Maximum Directed Path Packing Problem.

Zero Weights in Weak Efficient and Inefficient Points with AHP

In this paper an approach in data envelopment analysis dealing with evaluation of non – zero slacks was propounded. This approach intends that weight of inefficient and weak efficient points that have been evaluated as zero weight, be considered as positive weight, and also in this approach, the pareto efficiency evaluates the picture of this point. In this approach positive weights in the i...

Some zero-sum constants with weights

For an abelian group G, the Davenport constant D(G) is defined to be the smallest natural number k such that any sequence of k elements in G has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to (Z/...

The Maximum Number of Edges in a Strongly Multiplicative Graph

Improved Approximation Algorithms for Metric Maximum ATSP and Maximum 3-Cycle Cover Problems

We consider an APX-hard variant (∆-Max-ATSP) and an APX-hard relaxation (Max-3-DCC) of the classical traveling salesman problem. We present a 31 40 -approximation algorithm for ∆-Max-ATSP and a 34 -approximation algorithm for Max-3-DCC with polynomial running time. The results are obtained via a new way of applying techniques for computing undirected cycle covers to directed problems.