An FPT Algorithm for Matching Cut and d-Cut

An FPT Algorithm Beating 2-Approximation for k-Cut

In the k-Cut problem, we are given an edge-weighted graph G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k connected components. Prior work on this problem gives, for all h ∈ [2, k], a (2 − h/k)-approximation algorithm for k-cut that runs in time n. Hence to get a (2− ε)-approximation algorithm for some absolute constant ε, the best runtim...

An Efficient Approximation Algorithm for Max-Cut

Significant research effort has been devoted in the study of approximation algorithms for NP-hard problems. Ap-proximation algorithm for Max-Cut problem with performance guarantee of 0. 87856 is long known. In this work we study balanced Max-Cut problem. We give a balancing factor ? for given ? such that the approximate solution is at least 0. 87856 times the optimal ?-balanced cut and it is it...

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G = (V , E), and g groups of vertices X1, . . . , Xg ⊆ V with each group Xi having a requirement ri between 0 and |Xi|, the goal is to find aminimum cost set of edges whose removal separates each group Xi into at least ri disconnected components. We give a tightΘ(log g) ap...

Approximation Algorithm for Maximum Cut

Pattern Matching as Cut Elimination

We present a typed pattern calculus with explicit pattern matching and explicit substitutions, where both the typing rules and the reduction rules are modeled on the same logical proof system, namely Gentzen sequent calculus for minimal logic. Our calculus is inspired by the Curry-Howard Isomorphism, in the sense that types, both for patterns and terms, correspond to propositions, terms corresp...