Related papers: Matroid Intersection under Restricted Oracles

There is a long list of open questions rooted in the same underlying problem: understanding the structure of bases or common bases of matroids. These conjectures suggest that matroids may possess much stronger structural properties than are…

Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…

Greedy minimum weight spanning tree packings have proven to be useful in connectivity-related problems. We study the process of greedy minimum weight base packings in general matroids and explore its applications. For general matroids, we…

In this paper we study a resource allocation problem that encodes correlation between items in terms of \conflict and maximizes the minimum utility of the agents under a conflict free allocation. Admittedly, the problem is computationally…

We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…

We study a particular graded ring structure on the set of all loopfree matroids on a fixed labeled ground set, which occurs naturally in tropical geometry. The product is given by matroid intersection and the additive structure is defined…

We study point-line configurations, their minimal matroids, and their associated circuit varieties. We present an algorithm for identifying the minimal matroids of these configurations with respect to dependency order, or equivalently, the…

We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…

We investigate the problem of constructing fault-tolerant bases in matroids. Given a matroid M and a redundancy parameter k, a k-fault-tolerant basis is a minimum-size set of elements such that, even after the removal of any k elements, the…

Causal inference in modern largescale systems faces growing challenges, including highdimensional covariates, multi-valued treatments, massive observational (OBS) data, and limited randomized controlled trial (RCT) samples due to cost…

Distributed processing frameworks, such as MapReduce, Hadoop, and Spark are popular systems for processing large amounts of data. The design of efficient algorithms in these frameworks is a challenging problem, as the systems both require…

We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference…

Let M be a matroid on ground set E. A subset l of E is called a `line' when its rank equals 1 or 2. Given a set L of lines, a `fractional matching' in (M,L) is a nonnegative vector x indexed by the lines in L, that satisfies a system of…

Joint channel and rate allocation with power minimization in orthogonal frequency-division multiple access (OFDMA) has attracted extensive attention. Most of the research has dealt with the development of sub-optimal but low-complexity…

Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…

One of the classic problems in online decision-making is the *secretary problem* where to goal is to maximize the probability of choosing the largest number from a randomly ordered sequence. A natural extension allows selecting multiple…

We study the pure exploration problem subject to a matroid constraint (Best-Basis) in a stochastic multi-armed bandit game. In a Best-Basis instance, we are given $n$ stochastic arms with unknown reward distributions, as well as a matroid…

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…

We consider the budgeted matroid independent set problem. The input is a ground set, where each element has a cost and a non-negative profit, along with a matroid over the elements and a budget. The goal is to select a subset of elements…

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…