Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
Knapsack problems give a simple framework for decision making. A classical example is the min-knapsack problem (MinKnap): choose a subset of items with minimum total cost, whose total profit is above a given threshold. While this model successfully general ...
We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with a(n) memory per machine, that compute a maximal independent set, a 1 + epsilon approximation of maximum matching, and a 2 + epsilon approximation of minimum ve ...
2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...
In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...
The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...
State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be appr ...
Background: The gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the b ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
For a graph G, let nu(s)(G) be the strong matching number of G. We prove the sharp bound nu(s)(G) >= n(G)/9 for every graph G of maximum degree at most 4 and without isolated vertices that does not contain a certain blown-up 5-cycle as a component. This re ...
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a d ...
