The second volume of “Advancing Uncertain Combinatorics through Graphization,
Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” …

The goal of this textbook is twofold. First, the book serves as an introduction to the field of
parameterized algorithms and complexity accessible to graduate students and advanced …

We consider the problem of computing the rank of an m× n matrix A over a field. We present
a randomized algorithm to find a set of r= rank (A) linearly independent columns in Õ (| A|+ r …

In this paper we consider the classic matroid intersection problem: given two matroids M
1=(V, I 1) and M 2=(V, I 2) defined over a common ground set V, compute a set S∈ I 1∩ I 2 …

We consider the classical matroid matching problem. Unweighted matroid matching for
linear matroids was solved by Lovasz, and the problem is known to be intractable for …

We study a natural generalization of the maximum weight many-to-one matching problem.
We are given an undirected bipartite graph G=(A\, ̇ ∪\, P, E) G=(A∪˙ P, E) with weights on …

The matroid parity (or matroid matching) problem, introduced as a common generalization of
matching and matroid intersection problems, is so general that it requires an exponential …

Matrix representations are a powerful tool for designing efficient algorithms for combinatorial
optimization problems such as matching, and linear matroid intersection and parity. In this …

In this paper, we propose new exact and approximation algorithms for the weighted matroid
intersection problem. Our exact algorithm is faster than previous algorithms when the largest …

Abstract Let f: 2 N→ Z+ be a polymatroid (an integer-valued non-decreasing submodular set
function with f (∅)= 0). A k-polymatroid satisfies that f (e)≤ k for all e∈ N. We call S⊆ N …