Related papers: Dynamic Matroids: Base Packing and Covering
This paper initiates the studies of parallel algorithms for core maintenance in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which are widely used in large-scale graph analytics. The core…
We show that finding lexicographically minimal $n$ bases in a matroid can be done in polynomial time in the oracle model. This follows from a more general result that the shifted problem over a matroid can be solved in polynomial time as…
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
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…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
We present the first (randomized) parallel dynamic algorithm for maximal matching, which can process an arbitrary number of updates simultaneously. Given a batch of edge deletion or insertion updates to the graph, our parallel algorithm…
The basis exchange axiom has been a driving force in the development of matroid theory. However, the axiom gives only a local characterization of the relation of bases, which is a major stumbling block to further progress, and providing a…
Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
Querying complex models for precise information (e.g. traffic models, database systems, large ML models) often entails intense computations and results in long response times. Thus, weaker models which give imprecise results quickly can be…
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
Accurate maps are a prerequisite for virtually all mobile robot tasks. Most state-of-the-art maps assume a static world; therefore, dynamic objects are filtered out of the measurements. However, this division ignores movable but non-moving…
We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of $n$ nodes is vertex-partitioned among $k$ players that…
Dynamic graph algorithms have seen significant theoretical advancements, but practical evaluations often lag behind. This work bridges the gap between theory and practice by engineering and empirically evaluating recently developed…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and…
We give new characterizations for the class of uniformly dense matroids and study applications of these characterizations to graphic and real representable matroids. We show that a matroid is uniformly dense if and only if its base polytope…
Consider a matroid equipped with a labeling of its ground set to an abelian group. We define the label of a subset of the ground set as the sum of the labels of its elements. We study a collection of problems on finding bases and common…
The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially…