Oracle Tractability of Skew Bisubmodular Functions

TL;DR

This paper introduces a convex extension called Lovász extension for skew bisubmodular functions and proves that these functions can be minimized in polynomial time using an oracle.

Contribution

It presents the first polynomial-time minimization method for skew bisubmodular functions via a novel Lovász extension.

Findings

Skew bisubmodular functions can be minimized in polynomial time.

A convex Lovász extension is constructed for these functions.

The approach generalizes submodular minimization techniques.

Abstract

In this paper we consider skew bisubmodular functions as introduced in [9]. We construct a convex extension of a skew bisubmodular function which we call Lov\'asz extension in correspondence to the submodular case. We use this extension to show that skew bisubmodular functions given by an oracle can be minimised in polynomial time.