arXiv subjects

Benjamin Moseley

Publications and source records attributed to Benjamin Moseley.

At least 19 recordsLinked to original sources

arXiv2026

Online Correlation Clustering with Metric Weights

The standard online version of correlation clustering is prohibitively hard, as even randomized algorithms cannot achieve competitive ratio better than $\Omega(n)$. Prior works bypass this lower bound by relaxing the online model through recourse, random arrival order, or seeding the algorithm with an offline sample of the underlying input. We instead ask whether additional structure in the input itself can overcome this lower bound. We study weighted correlation clustering under probability constraints, where $w^+_{uv}+w^-_{uv}=1$ for every $uv$ edge, and triangle inequality constraints, where the negative weights $w^-$ satisfy triangle inequality. While this version of correlation clustering is well-studied in the offline setting, we initiate its online study and give a deterministic online algorithm that maintains a clustering whose total weighted disagreement cost is within an $O(1)$ factor of the offline optimum, against adversarial arrival order. This is the first constant-competitive online algorithm for a natural minimization variant of correlation clustering in the fully online model, and shows that metric consistency on the edge weights separates tractable from intractable online instances.

cs.DS↗

arXiv2026

Matroid Contention Resolution with Concentration

Contention resolution schemes (CRS) are a fundamental and widely applied tool for rounding fractional solutions subject to combinatorial constraints. However, the known analyses of CRS generally only guarantee lower bounds on the expected value and concentration on the upper tail, but no concentration on the lower tail. Thus, CRS are generally not applicable to problems that contain covering constraints, since certifying a covering constraint holds requires a lower tail bound. Our main contribution is to derive lower tail bounds for the output of a particular contention resolution scheme, the random-order CRS of Adamczyk and W{\l}odarczyk, which we call AW. We show that every linear function of the rounded solution attains a constant fraction of its expectation with a failure probability that is dimension-free, depending only on the expected value and on the number of matroids, but not on the size of the ground set. Our analysis is driven by a new property we call \emph{strong $\lambda$-boundedness}, which strengthens the known $\lambda$-boundedness of AW by providing two-sided control on how rounding propagates between elements. We then introduce a random process capturing AW, a \emph{sequential selection process}, that may be of independent interest. We prove lower tail bounds for any strongly $\lambda$-bounded sequential selection process. To demonstrate the applicability of our new tail bounds, we apply them to two problems involving covering constraints. The first result is an $O(k \log k)$-approximation for $k$-matroid intersection coloring (improving the prior $O(k^2)$) when the chromatic number of at least one matroid is $\Omega(k^3 \log n)$, where $n$ is the number of elements. The second is the first bicriteria approximation algorithm for monotone submodular maximization under $k$ matroid constraints together with packing and covering constraints.

cs.DS↗

arXiv2026

Bayesian Probing on Graphs

We introduce a stochastic probing problem with correlated items. In our model, which we call Bayesian Probing, the correlations are modeled by an underlying graph $G$. Each vertex is independently active with a known probability. Each item corresponds to an edge in the graph. Probing an edge has some cost, gives some reward if both endpoints are active, and also reveals the state of its endpoints. Hence a probe induces a Bayesian update on the remaining edges. The goal is to adaptively probe items/edges subject to a knapsack constraint to maximize the expected total reward obtained from the probed edges. Bayesian Probing generalizes stochastic knapsack and stochastic probing by allowing correlations between items. Moreover, it gives a tractable model for the Bayesian Active Search problem, a popular problem considered in the machine learning community. In Bayesian Active Search, the goal is to find items in a particular class by adaptively probing at most, say $k$, items. Given a prior distribution over items, we want to compute a Bayesian policy to maximize the number of such items found. For this general problem with arbitrary priors, there are strong lower bounds on efficiently computing good policies. In this paper, we design efficient approximation algorithms for Bayesian Probing. These results give the first efficient approximation algorithms for Bayesian Active Search, for a class of practically-relevant prior distributions.

cs.DS↗

arXiv2026

No, Cake Cutting Really is a Piece of Cake

We design and analyze a deterministic cake cutting algorithm that achieves proportional fairness using a linear number of cuts. The best previous upper bound on the number of cuts for a deterministic algorithm was $O(n \log n)$, which was obtained by a natural divide-and-conquer algorithm due to Even and Paz. It has long been conjectured that $O(n \log n)$ cuts was optimal for a deterministic algorithm.

cs.GT↗

arXiv2026

Approximation Algorithms for Matroid-Intersection Coloring with Applications to Rota's Basis Conjecture

We study algorithmic matroid intersection coloring. Given $k$ matroids on a common ground set $U$ of $n$ elements, the goal is to partition $U$ into the fewest number of color classes, where each color class is independent in all matroids. It is known that $2\chi_{\max}$ colors suffice to color the intersection of two matroids, $(2k-1)\chi_{\max}$ colors suffice for general $k$, where $\chi_{\max}$ is the maximum chromatic number of the individual matroids. However, these results are non-constructive, leveraging techniques such as topological Hall's theorem and Sperner's Lemma. We provide the first polynomial-time algorithms to color two or more general matroids where the approximation ratio depends only on $k$ and, in particular, is independent of $n$. For two matroids, we constructively match the $2\chi_{\max}$ existential bound, yielding a 2-approximation for the Matroid Intersection Coloring problem. For $k$ matroids we achieve a $(k^2-k)\chi_{\max}$ coloring, which is the first $O(1)$-approximation for constant $k$. Our approach introduces a novel matroidal structure we call a \emph{flexible decomposition}. We use this to formally reduce general matroid intersection coloring to graph coloring while avoiding the limitations of partition reduction techniques, and without relying on non-constructive topological machinery. Furthermore, we give a \emph{fully polynomial randomized approximation scheme} (FPRAS) for coloring the intersection of two matroids when $\chi_{\max}$ is large. This yields the first polynomial-time constructive algorithm for an asymptotic variant of Rota's Basis Conjecture. This constructivizes Montgomery and Sauermann's recent asymptotic breakthrough and generalizes it to arbitrary matroids.

cs.DS↗

arXiv2026

Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

In this paper, we study the fundamental problem of finding a stable matching in two-sided matching markets. In the classic variant, it is assumed that both sides of the market submit a ranked list of all agents on the other side. However, in large matching markets such as the National Resident Matching Program (NRMP), it is infeasible for hospitals to interview or mutually rank each resident. In this paper, we study the stable matching problem with truncated preference lists. In particular, we assume that, based on historical datasets, each hospital has a predicted rank of its likely match and only ranks residents within a bounded interval around that prediction. We use the algorithms-with-predictions framework and show that the classic deferred-acceptance (DA) algorithm used to compute stable matchings is robust to such truncation. We present two algorithms and theoretically and empirically evaluate their performance. Our results show that even with reasonably accurate predictions, it is possible to significantly cut down on both instance size (the length of preference lists) as well as the number of proposals made. These results explain the practical success of the DA algorithm and connect market design to the emerging theory of algorithms with predictions.

cs.GT↗

arXiv2026

Minimizing Completion Times of Stochastic Jobs on Parallel Machines is Hard

This paper considers the scheduling of stochastic jobs on parallel identical machines to minimize the expected total weighted completion time. While this is a classical problem with a significant body of research on approximation algorithms over the past two decades, constant-factor performance guarantees are currently known only under very restrictive assumptions on the input distributions, even when all job weights are identical. This algorithmic difficulty is striking given the lack of corresponding complexity results: to date, it is conceivable that the problem could be solved optimally in polynomial time. We address this gap with hardness results that demonstrate the problem's inherent intractability. For the special case of discrete two-point processing time distributions and unit weights, we prove that deciding whether there exists a scheduling policy with expected cost at most a given threshold is #P-hard. Furthermore, we show that evaluating the expected objective value of the standard (W)SEPT list scheduling policy is itself #P-hard. These are the first hardness results for scheduling independent stochastic jobs and min-sum objective that do not merely rely on the intractability of the underlying deterministic counterparts.

cs.DS↗

arXiv2025

Online Correlation Clustering: Simultaneously Optimizing All $\ell_p$-norms

The $\ell_p$-norm objectives for correlation clustering present a fundamental trade-off between minimizing total disagreements (the $\ell_1$-norm) and ensuring fairness to individual nodes (the $\ell_\infty$-norm). Surprisingly, in the offline setting it is possible to simultaneously approximate all $\ell_p$-norms with a single clustering. Can this powerful guarantee be achieved in an online setting? This paper provides the first affirmative answer. We present a single algorithm for the online-with-a-sample (AOS) model that, given a small constant fraction of the input as a sample, produces one clustering that is simultaneously $O(\log^4 n)$-competitive for all $\ell_p$-norms with high probability, $O(\log n)$-competitive for the $\ell_\infty$-norm with high probability, and $O(1)$-competitive for the $\ell_1$-norm in expectation. This work successfully translates the offline "all-norms" guarantee to the online world. Our setting is motivated by a new hardness result that demonstrates a fundamental separation between these objectives in the standard random-order (RO) online model. Namely, while the $\ell_1$-norm is trivially $O(1)$-approximable in the RO model, we prove that any algorithm in the RO model for the fairness-promoting $\ell_\infty$-norm must have a competitive ratio of at least $\Omega(n^{1/3})$. This highlights the necessity of a different beyond-worst-case model. We complement our algorithm with lower bounds, showing our competitive ratios for the $\ell_1$- and $\ell_\infty$- norms are nearly tight in the AOS model.

cs.LG↗

arXiv2025

Efficiently Coloring the Intersection of a General Matroid and Combinatorial Matroids

This paper shows a polynomial-time algorithm that, given a general matroid $M_1$ and $k-1$ partition matroids $ M_2, \ldots, M_k$, produces a coloring of the intersection $M = \cap_{i=1}^k M_i$ using at most $1+\sum_{i=1}^k \left(\chi(M_i) -1\right)$ colors. This is the first polynomial-time $O(k)$-approximation algorithm for matroid intersection coloring where one of the matroids may be a general matroid. Leveraging the fact that most of the standard combinatorial matroids reduce to partition matroids at a loss of a factor of two in the chromatic number, this algorithm also yields a polynomial-time $O(k)$-approximation algorithm for matroid intersection coloring in the case where each of the matroids $ M_2, \ldots, M_k$ are one of these standard combinatorial types. Even when $k = 2$, the previous best-known approximation ratio was $O(\log n)$ via a reduction to Set Cover.

cs.DS↗

arXiv2025

Competitive Online Transportation Simplified

The setting for the online transportation problem is a metric space $M$, populated by $m$ parking garages of varying capacities. Over time cars arrive in $M$, and must be irrevocably assigned to a parking garage upon arrival in a way that respects the garage capacities. The objective is to minimize the aggregate distance traveled by the cars. In 1998, Kalyanasundaram and Pruhs conjectured that there is a $(2m-1)$-competitive deterministic algorithm for the online transportation problem, matching the optimal competitive ratio for the simpler online metric matching problem. Recently, Harada and Itoh presented the first $O(m)$-competitive deterministic algorithm for the online transportation problem. Our contribution is an alternative algorithm design and analysis that we believe is simpler.

cs.DS↗

arXiv2025

Robust Gittins for Stochastic Scheduling

A common theme in stochastic optimization problems is that, theoretically, stochastic algorithms need to "know" relatively rich information about the underlying distributions. This is at odds with most applications, where distributions are rough predictions based on historical data. Thus, commonly, stochastic algorithms are making decisions using imperfect predicted distributions, while trying to optimize over some unknown true distributions. We consider the fundamental problem of scheduling stochastic jobs preemptively on a single machine to minimize expected mean completion time in the setting where the scheduler is only given imperfect predicted job size distributions. If the predicted distributions are perfect, then it is known that this problem can be solved optimally by the Gittins index policy. The goal of our work is to design a scheduling policy that is robust in the sense that it produces nearly optimal schedules even if there are modest discrepancies between the predicted distributions and the underlying real distributions. Our main contributions are: (1) We show that the standard Gittins index policy is not robust in this sense. If the true distributions are perturbed by even an arbitrarily small amount, then running the Gittins index policy using the perturbed distributions can lead to an unbounded increase in mean completion time. (2) We explain how to modify the Gittins index policy to make it robust, that is, to produce nearly optimal schedules, where the approximation depends on a new measure of error between the true and predicted distributions that we define. Looking forward, the approach we develop here can be applied more broadly to many other stochastic optimization problems to better understand the impact of mispredictions, and lead to the development of new algorithms that are robust against such mispredictions.

cs.DS↗

arXiv2025

Efficient Algorithms for Cardinality Estimation and Conjunctive Query Evaluation With Simple Degree Constraints

Cardinality estimation and conjunctive query evaluation are two of the most fundamental problems in database query processing. Recent work proposed, studied, and implemented a robust and practical information-theoretic cardinality estimation framework. In this framework, the estimator is the cardinality upper bound of a conjunctive query subject to ``degree-constraints'', which model a rich set of input data statistics. For general degree constraints, computing this bound is computationally hard. Researchers have naturally sought efficiently computable relaxed upper bounds that are as tight as possible. The polymatroid bound is the tightest among those relaxed upper bounds. While it is an open question whether the polymatroid bound can be computed in polynomial-time in general, it is known to be computable in polynomial-time for some classes of degree constraints. Our focus is on a common class of degree constraints called simple degree constraints. Researchers had not previously determined how to compute the polymatroid bound in polynomial time for this class of constraints. Our first main result is a polynomial time algorithm to compute the polymatroid bound given simple degree constraints. Our second main result is a polynomial-time algorithm to compute a ``proof sequence'' establishing this bound. This proof sequence can then be incorporated in the PANDA-framework to give a faster algorithm to evaluate a conjunctive query. In addition, we show computational limitations to extending our results to broader classes of degree constraints. Finally, our technique leads naturally to a new relaxed upper bound called the {\em flow bound}, which is computationally tractable.

cs.DB↗

arXiv2025

Faster Global Minimum Cut with Predictions

Global minimum cut is a fundamental combinatorial optimization problem with wide-ranging applications. Often in practice, these problems are solved repeatedly on families of similar or related instances. However, the de facto algorithmic approach is to solve each instance of the problem from scratch discarding information from prior instances. In this paper, we consider how predictions informed by prior instances can be used to warm-start practical minimum cut algorithms. The paper considers the widely used Karger's algorithm and its counterpart, the Karger-Stein algorithm. Given good predictions, we show these algorithms become near-linear time and have robust performance to erroneous predictions. Both of these algorithms are randomized edge-contraction algorithms. Our natural idea is to probabilistically prioritize the contraction of edges that are unlikely to be in the minimum cut.

cs.DS↗

arXiv2025

Incremental Approximate Single-Source Shortest Paths with Predictions

The algorithms-with-predictions framework has been used extensively to develop online algorithms with improved beyond-worst-case competitive ratios. Recently, there is growing interest in leveraging predictions for designing data structures with improved beyond-worst-case running times. In this paper, we study the fundamental data structure problem of maintaining approximate shortest paths in incremental graphs in the algorithms-with-predictions model. Given a sequence $\sigma$ of edges that are inserted one at a time, the goal is to maintain approximate shortest paths from the source to each vertex in the graph at each time step. Before any edges arrive, the data structure is given a prediction of the online edge sequence $\hat{\sigma}$ which is used to ``warm start'' its state. As our main result, we design a learned algorithm that maintains $(1+\epsilon)$-approximate single-source shortest paths, which runs in $\tilde{O}(m \eta \log W/\epsilon)$ time, where $W$ is the weight of the heaviest edge and $\eta$ is the prediction error. We show these techniques immediately extend to the all-pairs shortest-path setting as well. Our algorithms are consistent (performing nearly as fast as the offline algorithm) when predictions are nearly perfect, have a smooth degradation in performance with respect to the prediction error and, in the worst case, match the best offline algorithm up to logarithmic factors. As a building block, we study the offline incremental approximate single-source shortest-paths problem. In this problem, the edge sequence $\sigma$ is known a priori and the goal is to efficiently return the length of the shortest paths in the intermediate graph $G_t$ consisting of the first $t$ edges, for all $t$. Note that the offline incremental problem is defined in the worst-case setting (without predictions) and is of independent interest.

cs.DS↗

arXiv2024

Binary Search with Distributional Predictions

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first distributionally-robust algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

cs.LG↗

arXiv2024

Putting Off the Catching Up: Online Joint Replenishment Problem with Holding and Backlog Costs

We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier for multiple items over time: each request is for some item that the retailer needs in the future, and has an arrival time and a soft deadline. If a request is served before its deadline, the retailer pays a holding cost per unit of the item until the deadline. However, if a request is served after its deadline, the retailer pays a backlog cost per unit. Each service incurs a fixed joint service cost and a fixed item-dependent cost for every item included in a service. These fixed costs are the same irrespective of the units of each item ordered. The goal is to schedule services to satisfy all the online requests while minimizing the sum of the service costs, the holding costs, and the backlog costs. Constant competitive online algorithms have been developed for two special cases: the make-to-order version when the deadlines are equal to arrival times (Buchbinder et al., 2013), and the make-to-stock version with hard deadlines with zero holding costs (Bienkowski et al., 2014). Our general model with holding and backlog costs has not been investigated earlier, and no online algorithms are known even in the make-to-stock version with hard deadlines and non-zero holding costs. We develop a new online algorithm for the general version of online JRP with both holding and backlog costs and establish that it is 30-competitive. Along the way, we develop a 3-competitive algorithm for the single-item case that we build on to get our final result. Our algorithm uses a greedy strategy and its competitiveness is shown using a dual fitting analysis.

cs.DS↗

arXiv2024

Asymptotically Optimal Scheduling of Multiple Parallelizable Job Classes

Modern computing workloads are often composed of parallelizable jobs. A parallelizable job can be completed more quickly when run on additional servers. However, each job can only use a limited number of servers, known as its parallelizability level, which is determined by the type of computation the job performs and how it is implemented. Workloads generally consist of multiple job classes, where jobs from different classes have different parallelizability levels and follow different job size (service requirement) distributions. This paper considers scheduling parallelizable jobs belonging to an arbitrary number of job classes. Given a limited number of servers, we must allocate servers across a stream of arriving jobs to minimize mean response time -- the average time from when a job arrives to the system until it completes. We find that in lighter-load scaling regimes (i.e., Sub-Halfin-Whitt), the optimal allocation policy is Least-Parallelizable-First (LPF), which prioritizes jobs from the least parallelizable job classes regardless of their size distributions. By contrast, we find that in the heavier-load regimes (i.e., Super-NDS), the optimal allocation policy prioritizes jobs with the Shortest Expected Remaining Processing Time (SERPT). We also develop policies that are asymptotically optimal when the scaling regime is not known a priori.

cs.PF↗

arXiv2024

Best of Many in Both Worlds: Online Resource Allocation with Predictions under Unknown Arrival Model

Online decision-makers often obtain predictions on future variables, such as arrivals, demands, inventories, and so on. These predictions can be generated from simple forecasting algorithms for univariate time-series, all the way to state-of-the-art machine learning models that leverage multiple time-series and additional feature information. However, the prediction accuracy is unknown to decision-makers a priori, hence blindly following the predictions can be harmful. In this paper, we address this problem by developing algorithms that utilize predictions in a manner that is robust to the unknown prediction accuracy. We consider the Online Resource Allocation Problem, a generic model for online decision-making, in which a limited amount of resources may be used to satisfy a sequence of arriving requests. Prior work has characterized the best achievable performances when the arrivals are either generated stochastically (i.i.d.) or completely adversarially, and shown that algorithms exist which match these bounds under both arrival models, without ``knowing'' the underlying model. To this backdrop, we introduce predictions in the form of shadow prices on each type of resource. Prediction accuracy is naturally defined to be the distance between the predictions and the actual shadow prices. We tightly characterize, via a formal lower bound, the extent to which any algorithm can optimally leverage predictions (that is, to ``follow'' the predictions when accurate, and ``ignore'' them when inaccurate) without knowing the prediction accuracy or the underlying arrival model. Our main contribution is then an algorithm which achieves this lower bound. Finally, we empirically validate our algorithm with a large-scale experiment on real data from the retailer H&M.

math.OC↗