arXiv subjects

Helia Niaparast

Publications and source records attributed to Helia Niaparast.

5 recordsLinked to original sources

arXiv2026

Incremental Strongly Connected Components with Predictions

Algorithms with predictions is a growing area that aims to leverage machine-learned predictions to design faster beyond-worst-case algorithms. In this paper, we use this framework to design a learned data structure for the incremental strongly connected components (SCC) problem. In this problem, the $n$ vertices of a graph are known a priori and the $m$ directed edges arrive over time. The goal is to efficiently maintain the strongly connected components of the graph after each insert. Our algorithm receives a possibly erroneous prediction of the edge sequence and uses it to precompute partial solutions to support fast inserts. We show that our algorithm achieves nearly optimal bounds with good predictions and its performance smoothly degrades with the prediction error. We also implement our data structure and perform experiments on real datasets. Our empirical results show that the theory is predictive of practical runtime improvements.

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↗

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 $σ$ 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 $\hatσ$ which is used to ``warm start'' its state. As our main result, we design a learned algorithm that maintains $(1+ε)$-approximate single-source shortest paths, which runs in $\tilde{O}(m η\log W/ε)$ time, where $W$ is the weight of the heaviest edge and $η$ 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 $σ$ 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↗

arXiv2023

Tight Bounds on the Chromatic Edge Stability Index of Graphs

The chromatic edge stability index $\mathrm{es}_{χ'}(G)$ of a graph $G$ is the minimum number of edges whose removal results in a graph with smaller chromatic index. We give best-possible upper bounds on $\mathrm{es}_{χ'}(G)$ in terms of the number of vertices of degree $Δ(G)$ (if $G$ is Class 2), and the numbers of vertices of degree $Δ(G)$ and ${Δ(G)-1}$ (if $G$ is Class 1). If $G$ is bipartite we give an exact expression for $\mathrm{es}_{χ'}(G)$ involving the maximum size of a matching in the subgraph induced by vertices of degree $Δ(G)$. Finally, we consider whether a minimum mitigating set, that is a set of size $\mathrm{es}_{χ'}(G)$ whose removal reduces the chromatic index, has the property that every edge meets a vertex of degree at least $Δ(G)-1$; we prove that this is true for some minimum mitigating set of $G$, but not necessarily for every minimum mitigating set of $G$.

math.CO↗