Matroid
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Related Articles from SNS
Entropy Functions on Two-Dimensional Faces of Polymatroid Region Spanned by a Matroid and a Rank-One Matroid
Announce Type: replace Abstract: Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this paper, we characterize entropy functions on 2-dimensional faces of polymatroidal region of degree n spanned by a matroid and a rank-1 matroid.
Multiagent Matroid Upgrading: Greedy is Fair and Efficient
Announce Type: new Abstract: This paper introduces a general multiagent matroid upgrading problem that models a broad class of real-world resource allocation tasks. In this setting, there are multiple agents and a ground set of elements, where each element is assigned to a specific agent and has two associated costs: a default cost and a reduced (upgraded) cost. Upgrading an element lowers its cost to the upgraded value, while non-upgraded elements retain their default costs.
Minibatch Selection via Partition Matroid Constrained Gradient Matching
Announce Type: new Abstract: Training large language models (LLMs) on heterogeneous data requires selecting minibatches that balance convergence speed with coverage across domains. Existing methods either select samples independently within each domain or rely on computationally expensive proxy models to learn continuous domain weights. We propose PartitionSel, a cross-domain minibatch selection approach that maximizes a validation-guided gradient-matching utility under per-domain budgets...
The Polymatroid Representation of a Greedoid, and Associated Galois Connections
Announce Type: replace-cross Abstract: A greedoid is a generalization of a matroid allowing for more flexible analyses and modeling of combinatorial optimization problems. However, these structures decimate many matroid properties contributing to their pervasive nature. A polymatroid greedoid
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $RM_q(2,2)$
arXiv:2408.02548v3 Announce Type: replace-cross Abstract: We determine all the Betti numbers of the $q$-ary second order Reed-Muller codes of length $q^2$, and also of the elongations of matroids associated to these codes. We then use it to determine the higher weight spectra of these codes. As a special case, we recover some results of Kaplan and Matei about counting certain curves over finite fields with prescribed rational intersection points.
Maximum Matching and Related Problems in Catalytic Logspace
arXiv:2604.24275v2 Announce Type: replace Abstract: Understanding the power of space-bounded computation with access to catalytic space has been an important theme in complexity theory over the recent years. One of the key algorithmic results in this area is that bipartite maximum matching can be computed in catalytic logspace with a polynomial-time bound, Agarwala and Mertz (2025). In this paper, we show that we can construct a \emph{maximum matching} in \emph{general graphs} in CL, and, in...
A General Framework for Dynamic Consistent Submodular Maximization
Announce Type: new Abstract: Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully...