Related papers: Matroid Algorithms Under Size-Sensitive Independen…
In the matroid intersection problem, we are given two matroids of rank $r$ on a common ground set $E$ of $n$ elements and the goal is to find the maximum set that is independent in both matroids. In this note, we show that Cunningham's…
One of the most intriguing unsolved questions of matroid optimization is the characterization of the existence of $k$ disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures…
The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and…
We consider the following Stochastic Boolean Function Evaluation problem, which is closely related to several problems from the literature. A matroid $\mathcal{M}$ (in compact representation) on ground set $E$ is given, and each element…
We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on…
In the matroid secretary problem, the elements of a matroid $\mathcal{M}$ arrive in random order. Once we observe an item we need to irrevocably decide whether or not to accept it. The set of selected elements should form an independent set…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
We study a type of reverse (procurement) auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same…
We study the Maximum Independent Set (MIS) problem on general graphs within the framework of learning-augmented algorithms. The MIS problem is known to be NP-hard and is also NP-hard to approximate to within a factor of $n^{1-\delta}$ for…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
In this study, we consider a class of linear matroid interdiction problems, where the feasible sets for the upper-level decision-maker (referred to as a leader) and the lower-level decision-maker (referred to as a follower) are induced by…
In this paper, we consider dynamic matroids, where elements can be inserted to or deleted from the ground set over time. The independent sets change to reflect the current ground set. As matroids are central to the study of many…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
In linear combinatorial optimization, we aim to find $S^* = \arg\min_{S \in \mathcal{F}} \langle w,\mathbf{1}_S \rangle$ for a family $\mathcal{F} \subseteq 2^U$ over a ground set $U$ of $n$ elements. Traditionally, $w$ is known or…
We study the following Independent Stable Set problem. Let G be an undirected graph and M = (V(G),I) be a matroid whose elements are the vertices of G. For an integer k\geq 1, the task is to decide whether G contains a set S\subseteq V(G)…
In the matroid buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to a matroid constraint on the set of accepted bids. Decisions to reject bids are…
We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful…
Submodular function minimization (SFM) and matroid intersection are fundamental discrete optimization problems with applications in many fields. It is well known that both of these can be solved making $\mathrm{poly}(N)$ queries to a…