We consider the problem of locating a template as a subimage of a larger image. Computing the maxima of the correlation function solves this problem classically. Since the correlation can be calculated with the Fourier transform this problem is a good candidate for a superior quantum algorithmic solution. We outline how such an algorithm would work.

The Maximum Carpool Matching problem is a star packing problem in directed graphs. Formally, given a directed graph G = (V,A), a capacity function c : V → N, and a weight function w : A → R+, a carpool matching is a subset of arcs, M ⊆ A, such that every v ∈ V satisfies: (i) din M (v) · dout M (v) = 0, (ii) din M (v) ≤ c(v), and (iii) dout M (v) ≤ 1. A vertex v for which dout M (v) = 1 is a pas...

Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x, y) be log x/ log(x/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O( √ nW/k(n,W/N))-time algorithm for computing a maximum weight matching of G. T...

Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x, y) be log x/ log(x/y). We present a new decomposition theorem for maximum weight bipartite matchings and use it to design an O( √ nW/k(n,W/N))-time algorithm for computing a maximum weight matching of G. T...

A new approximation algorithm for maximum weighted matching in general edge-weighted graphs is presented. It calculates a matching with an edge weight of at least 1 2 of the edge weight of a maximum weighted matching. Its time complexity is O(jEj), with jEj being the number of edges in the graph. This improves over the previously known 1 2-approximation algorithms for maximum weighted matching ...

We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c > 0, independent of the value of c. This is contrary to the behavior of commonly used greedy matching heuristics which are known to have some range of c where they probably fail to ...

In this paper, we deal with both the complexity and the approximability of the labeled perfect matching problem in bipartite graphs. Given a simple graph G = (V, E) with n vertices with a color (or label) function L : E → {c1, . . . , cq}, the labeled maximum matching problem consists in finding a maximum matching on G that uses a minimum or a maximum number of colors.

We present Edmonds’ blossom shrinking algorithm for finding a maximum cardinality matching in a general graph. En route, we obtain an efficient algorithm for finding a minimum vertex cover in a bipartite graph and show that its size is equal to the size of the maximum matching in the graph. We also show that the size of a maximum matching in a general graph is equal to the size of a minimum odd...