An algorithmic Friedman-Pippenger theorem on tree embeddings and applications.
An alternative construction of normal numbers
A new class of -adic normal numbers is built recursively by using Eulerian paths in a sequence of de Bruijn digraphs. In this recursion, a path is constructed as an extension of the previous one, in such way that the -adic block determined by the path contains the maximal number of different -adic subblocks of consecutive lengths in the most compact arrangement. Any source of redundancy is avoided at every step. Our recursive construction is an alternative to the several well-known concatenative...
An approximation algorithm for the total covering problem
We introduce a 2-factor approximation algorithm for the minimum total covering number problem.
An attractive class of bipartite graphs
In this paper we propose a structural characterization for a class of bipartite graphs defined by two forbidden induced subgraphs. We show that the obtained characterization leads to polynomial-time algorithms for several problems that are NP-hard in general bipartite graphs.
An efficient algorithm for the transversal hypergraph generation.
An efficient -centroid location algorithm for cographs.
An evolutionary formulation of the crossing number problem.
An exact performance bound for an time greedy matching procedure.
Approximating clustering coefficient and transitivity.
Approximation algorithms for some graph partitioning problems.
Approximation algorithms for the traveling salesman problem with range condition
Approximation Algorithms for the Traveling Salesman Problem with Range Condition
We prove that the Christofides algorithm gives a approximation ratio for the special case of traveling salesman problem (TSP) in which the maximum weight in the given graph is at most twice the minimum weight for the odd degree restricted graphs. A graph is odd degree restricted if the number of odd degree vertices in any minimum spanning tree of the given graph is less than times the number of vertices in the graph. We prove that the Christofides algorithm is more efficient (in terms...
Approximations of weighted independent set and hereditary subset problems.
Arbology: Trees and pushdown automata
We present a unified and systematic approach to basic principles of Arbology, a new algorithmic discipline focusing on algorithms on trees. Stringology, a highly developed algorithmic discipline in the area of string processing, can use finite automata as its basic model of computation. For various kinds of linear notations of ranked and unranked ordered trees it holds that subtrees of a tree in a linear notation are substrings of the tree in the linear notation. Arbology uses pushdown automata...
Area Requirement and Symmetry Display of Planar Upward Drawings.