We consider the problem of estimating the size of a maximum matching when the edges are revealed in a streaming fashion. Consider a graph G = (V,E) with n vertices and m edges. The input stream is a permutation of edges S = 〈e1, . . . , em〉 chosen by an adversary. The goal is to output an estimation of the size of a maximum matching. The algorithm is only allowed to use a small amount of memory...

We provide a comprehensive study of natural graph optimization problem that arises from transition costs between incident edges. In the Minimum Scan Cover with Angular Costs (MSC), we are given $G$ is embedded in Euclidean space. The edges need to be scanned, i.e., probed both their vertices. order scan edge, two vertices face each other; changing heading vertex takes some time proportional cor...

A t-ruling set of a graph G = (V,E) is a vertex-subset S ⊆ V that is independent and satisfies the property that every vertex v ∈ V is at a distance of at most t from some vertex in S. A maximal independent set (MIS) is a 1-ruling set. The problem of computing an MIS on a network is a fundamental problem in distributed algorithms and the fastest algorithm for this problem is the O(logn)-round a...

The incidence coloring game has been introduced in [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980– 1987] as a variation of the ordinary coloring game. The incidence game chromatic number ιg(G) of a graph G is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on G. In [C. Charpentier and É. Sopen...