Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.09050

Efficient Algorithms for Online Subadditive Combinatorial Allocations

Calum MacRury·Rian Neogi·Kanstantsin Pashkovich·Sahil Singla·Siddharth M Sundaram·Chaitanya Swamy
View original source ↗Read source document ↗Export metadata ↓

Abstract

For the online combinatorial allocation problem with subadditive valuations, Correa and Cristi (STOC 2023) proved the existence of a $6$-competitive online algorithm, improving on the previous best $O(\log\!\log m)$-competitive online algorithm due to Dütting, Kesselheim, and Lucier (FOCS 2020), where $m$ is the number of items. However, Correa and Cristi's result is existential, and it was left open whether a constant competitive ratio is attainable via an efficient online algorithm that uses a polynomial number of demand oracle queries. In this work, we answer this affirmatively, giving an expected-polynomial-time $(6 + ε)$-competitive online algorithm for any constant $ε> 0$. Our techniques also recover, in the offline setting, the $(2 + ε)$-approximation result of Feige (STOC, 2006). Finally, when the buyers' valuations are drawn from identical distributions, we exploit symmetry to obtain an improved $(60/11+ε)$-competitive algorithm. Starting with the natural configuration LP relaxation for the problem, our main technical contribution is a recursive Bundle Score Generator (BSG) that resolves item conflicts by assigning correlated scores to the items requested by each buyer. Unlike the Random Score Generator whose existence is shown by Correa and Cristi, our BSG is efficiently computable in expected polynomial time. Moreover, it satisfies a stochastic dominance property that is sufficient to recover both Feige's offline result and Correa and Cristi's online result.

Explore related subjects

cs.DScs.GT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Calum MacRury, Rian Neogi, Kanstantsin Pashkovich, Sahil Singla, Siddharth M Sundaram, Chaitanya Swamy. 2026-10-09. Efficient Algorithms for Online Subadditive Combinatorial Allocations. https://arxiv.org/abs/2610.09050

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exact Algorithms for Distance to Unique Vertex Cover

Horiyama et al. (AAAI 2024) studied the problem of generating graph instances that possess a unique minimum vertex cover under specific conditions. Their approach involved pre-assigning certain vertices to be part of the solution or excluding them from it. Notably, for the \textsc{Vertex Cover} problem, pre-assigning a vertex is equivalent to removing it from the graph. Horiyama et al.~focused on maintaining the size of the minimum vertex cover after these modifications. In this work, we extend their study by relaxing this constraint: our goal is to ensure a unique minimum vertex cover, even if the removal of a vertex may not incur a decrease on the size of said cover. Surprisingly, our relaxation introduces significant theoretical challenges. We observe that the problem is $Σ^2_P$-complete, and remains so even for planar graphs of maximum degree 5. Nevertheless, we provide a linear time algorithm for trees, which is then further leveraged to show that MU-VC is in \textsf{FPT} when parameterized by the combination of treewidth and maximum degree. Finally, we show that MU-VC is in \textsf{XP} when parameterized by clique-width while it is fixed-parameter tractable (FPT) if we add the size of the solution as part of the parameter.

cs.DS↗
arXiv2026

Checking and producing word attractors

The article focuses on word (or string) attractors, which are sets of positions related to the text compression efficiency of the underlying word. The article presents two combinatorial algorithms based on Suffix automata or Directed Acyclic Word Graphs. The first algorithm decides in linear time whether a set of positions on the word is an attractor of the word. The second algorithm generates an attractor for a given word in a greedy manner. Although the problem of generating a smallest attractor is NP-hard, {the algorithm is efficient and produces very small attractors and even the smallest ones for several well-known infinite families of words.

cs.DS↗
arXiv2026

Faster and simpler traversal of 0/1-polytopes

Recently, Merino and Mütze (FOCS'23+SICOMP'24) presented an algorithm for computing a Hamilton path on the skeleton of any 0/1-polytope ${\rm conv}(X)$, where $X\subseteq\{0,1\}^n$. The algorithm uses as a black box an algorithm for solving the classical linear optimization problem $\min\{w\cdot x\mid x\in X\}$ for some weight vector $w\in\mathbb{R}^n$. The resulting delay per visited vertex on the Hamilton path is only by a $\log n$ factor larger than the time to solve one instance of the optimization algorithm. In this paper, we make the Hamilton path algorithm simpler and faster. Namely, we obtain an amortized delay that is only by a constant factor larger than the running time of the optimization algorithm, thus removing the $\log n$ factor. As concrete results, this yields improved algorithms for generating bases and independent sets in a matroid, spanning trees, forests, matchings and maximum matchings in a graph, vertex covers, minimum vertex covers, independent sets and maximum independent sets in a bipartite graph, and antichains, maximum antichains and ideals in a poset. All of these listings correspond to Hamilton paths on the corresponding polytopes. Furthermore, we obtain an $\mathcal{O}(t_{\rm LP})$ amortized delay algorithm for the vertex enumeration problem on 0/1-polytopes $\{x\in\mathbb{R}^n\mid Ax\leq b\}$, where $A\in \mathbb{R}^{m\times n}$ and $b\in\mathbb{R}^m$, and $t_{\rm LP}$ is the time needed to solve the linear program $\min\{w\cdot x\mid Ax\leq b\}$. This improves upon the $\mathcal{O}(t_{\rm LP} \log n)$ delay algorithm of Merino and Mütze, and the previous $\mathcal{O}(t_{\rm LP}\,n)$ delay algorithm of Bussieck and Lübbecke from 1998.

cs.DS↗