arXiv subjects

Mariia Anapolska

Publications and source records attributed to Mariia Anapolska.

3 recordsLinked to original sources

arXiv2025

Interval-Constrained Bipartite Matching over Time

Interval-constrained online bipartite matching problem frequently occurs in medical appointment scheduling: Unit-time jobs representing patients arrive online and are assigned to a time slot within their given feasible time interval. We consider a variant of this problem where reassignments are allowed and extend it by a notion of time that is decoupled from the job arrival events. As jobs appear, the current point in time gradually advances, and once the time of a slot is passed, the job assigned to it is fixed and cannot be reassigned anymore. We analyze two algorithms for the problem with respect to the resulting matching size and the number of reassignments they make. We show that FirstFit with reassignments according to the shortest augmenting path rule is $\frac{2}{3}$-competitive with respect to the matching cardinality, and that the bound is tight. For the number of reassignments performed by the algorithm, we show that it is in $Ω(n \log n)$ in the worst case, where $n$ is the number of patients or jobs on the online side. The competitive ratio remains bounded by $\frac{2}{3}$ if we restrict the algorithm to make only up to a constant number $k \geq 1$ of reassignments per job arrival. This fills the gap between the known optimal algorithm that makes no reassignments, which is $\frac{1}{2}$-competitive, on the one hand, and an earliest-deadline-first strategy (EDF), which we prove to obtain a maximum matching in this over-time framework, but which suffers $Ω(n^2)$ reassignments in the worst case, on the other hand. Further, we consider the setting in which the sets of feasible slots per job that are not intervals. We show that FirstFit remains $\frac{2}{3}$-competitive in this case, and that this is the best possible deterministic competitive ratio, while EDF loses its optimality.

cs.DS↗

arXiv2025

Minimum-Peak-Cost Flows Over Time

When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver parcels with a single truck over eight hours than to use two trucks for four hours, as long as the time suffices. To model such scenarios, we introduce the novel minimum peak cost flow over time problem, whose objective is to minimise the maximum cost at all points in time rather than minimising the integral of costs. We focus on minimising peak costs of temporally repeated flows. These are desirable for practical applications due to their simple structure. This yields the minimum-peak-cost temporally repeated flow problem (MPC-TRF). We show that the simple structure of temporally repeated flows comes with the drawback of arbitrarily bad approximation ratios compared to general flows over time. Furthermore, our complexity analysis shows the integral version of MPC-TRF is strongly NP-hard, even under strong restrictions. On the positive side, we identify two benign special cases: unit-cost series-parallel networks and networks with time horizon at least twice as long as the longest path in the network (with respect to the transit time). In both cases, we show that integral optimal flows if the desired flow value equals the maximum flow value and fractional optimal flows for arbitrary flow values can be found in polynomial time. For each of these cases, we provide an explicit algorithm that constructs an optimal solution.

cs.DS↗

arXiv2025

A Faster Parametric Search for the Integral Quickest Transshipment Problem

Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, runtime improvements are limited to general progress on submodular function minimization, which is an integral part of Hoppe and Tardos' algorithm. Yet, no structural improvements on their algorithm itself have been proposed. We replace two central subroutines in the algorithm with methods that require vastly fewer minimizations of submodular functions. This improves the state-of-the-art runtime from $ \tilde{O}(m^4 k^{15}) $ down to $ \tilde{O}(m^2 k^5 + m^4 k^2) $, where $ k $ is the number of terminals and $ m $ is the number of arcs.

cs.DS↗