When an aircraft is approaching airport, it gets a short time interval called slot by Air Traffic Control that can use to land. If the landing of delayed for some reason, loses its and Airline Operation Controllers have assign new one. However, slots are scarce resource airports and, in order avoid waits too long, regularly modify assignment aircraft. Due system implemented exchange slots, cont...

A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We consider the problem of finding a k-restricted simple 2-matching with a maximum number of edges, which is a relaxation of the problem of finding a Hamilton cycle in a graph. Our main result is a min-max theorem for the maxi...

Let G be an edge-weighted hypergraph on n vertices, m edges of size O(1), where the edges have real weights in an interval [1, W ]. We show that if we can approximate a maximum weight matching in G within factor α in time T (n,m,W ) then we can find a matching of weight at least (α − ǫ) times the maximum weight of a matching in G in time (ǫ) max 1≤q≤O(ǫ log n ǫ log ǫ−1 ) maxm1+...mq=m ∑q 1 T (n...

We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph G(V, E) are revealed in a streaming fashion. We analyze a variant of the previously best-known (4 + )-approximation algorithm due to Crouch and Stubbs (APPROX, 2014), and prove their conjecture that it achieves a tight approximation factor of 3.5+ . The algorithm splits the strea...

Let G = (V,E) be a graph with positive integral edge weights. Our problem is to find a matching of maximum weight in G. We present a simple iterative algorithm for this problem that uses a maximum cardinality matching algorithm as a subroutine. Using the current fastest maximum cardinality matching algorithms, we solve the maximum weight matching problem in O(W √ nm logn(n /m)) time, or in O(Wn...