arXiv subjects

Yu Cong

Publications and source records attributed to Yu Cong.

5 recordsLinked to original sources

arXiv2026

Integrality-Gap Bounds for Weighted Matchoids and Matroid Intersection

The weighted $k$-matroid intersection problem asks for a maximum-weight set that is independent in each of $k$ matroids on a common ground set. The natural LP relaxation optimizes over the intersection of the $k$ matroid independent set polytopes. It is conjectured that this LP has integrality gap at most $k-1$. The conjecture is known for $k\le3$, but for $k\ge4$ the best general upper bound was $k$. We improve this bound to $k-1+1/k$. More generally, we prove that the natural LP of a $p$-matchoid has integrality gap at most $p-1+1/p$, with a deterministic LP-relative algorithm attaining the same factor. The matchoid extension resolves the $p$-matchoid part of a conjecture of Lee, Sviridenko, and Vondrák; projective planes give explicit tight instances whenever one of order $p-1$ exists.

math.CO↗

arXiv2026

Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints

We consider a large-scale incentive allocation problem where the entire trade-off curve between budget and profit has to be maintained approximately at all times. The application originally comes from assigning coupons to users of ride-sharing apps, where each user can have a limit on the number of coupons assigned to them. We consider a more general form, where the coupons for each user form a matroid, and the set of coupons assigned to each user must be an independent set. We show the entire trade-off curve can be maintained approximately in near real time.

cs.DS↗

arXiv2026

Derandomizing Karger's Contraction Algorithm for Matroids

Karger's randomized contraction algorithm finds a minimum-weight cocircuit of a matroid whenever the cogirth-density ratio is bounded. We prove that the same hypothesis yields a deterministic algorithm with the same exponent. If every contraction minor of rank at least $r_0$ of a matroid $M$ has cogirth-density ratio at most $c$, then a minimum-weight cocircuit of $M$ is computable deterministically in $m^{O(r_0)} n^{O(c)}$ time when the contraction minors of bounded rank have at most $m$ parallel classes, by an algorithm that knows neither $r_0$ nor $c$. As a consequence, we give a deterministic algorithm computing the cogirth of rank-$p$ perturbed graphic matroids in $2^{O(p^2)} n^{O(1)}$ time, fixed-parameter tractable in $p$, settling the cogirth side of a question of Geelen and Kapadia (2018). The extensions of the contraction method carry over deterministically: enumerating all near-minimum 1-cocycles, computing a minimum-weight $k$-cocycle, and computing the Pareto frontier under several positive criteria.

cs.DS↗

arXiv2026

Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

cs.LG↗

arXiv2026

A Note on Interdiction of Linear Minimization Problems

Motivated by the FPTAS for connectivity interdiction of Huang et al. (IPCO'24), we isolate the part of the argument that does not use cuts. The setting is a minimization problem over a feasible-set family $\mathcal F$ with a linear objective $w(S)=\sum_{e\in S}w(e)$. After dualizing the interdiction budget, deletion can be absorbed into truncated weights $w_λ(e)=\min\{w(e),λc(e)\}$. At an optimal Lagrange multiplier $λ^*$, the unknown optimal interdiction witness is a strict $2$-approximate minimizer of the reweighted problem. Thus an exact algorithm can be obtained whenever one can optimize $w_{λ^*}$ over $\mathcal F$, enumerate all its $2$-approximate minimizers, and solve the remaining knapsack problem.

cs.DS↗