arXiv subjects

Igor Averbakh

Publications and source records attributed to Igor Averbakh.

4 recordsLinked to original sources

arXiv2026

Promoting Fair Online Resource Allocation with Indivisible Units

Allocating scarce, indivisible resources to diverse groups under uncertainty is a central challenge in operations research, where efficiency-focused methods often underserve marginalized populations. We study the Fair Online Resource Allocation with Indivisible Units (FORA-IU) problem, in which an unpredictable sequence of demands must be served from a strictly fixed inventory, and ask what fairness guarantees are achievable under different distributional and structural assumptions. We adopt a fairness criterion based on the expected filling ratio (FE-FR-beta), which balances each group's expected allocation against its expected demand and priority weight. We design online policies that calibrate acceptance probabilities to the remaining budget, analyze both arbitrary time-varying and stationary arrivals, introduce the Random Cyclic Blocks (RCB) algorithm tailored to the stationary case, and study the effect of restricting policies to all-or-nothing allocations. For arbitrary time-varying arrivals, our policy achieves the optimal universal fairness guarantee of 1/(1+R_beta), where R_beta denotes the priority-weighted system load. For time-invariant arrivals, RCB achieves the exact finite-horizon guarantee [1-(1-R_beta/T)^T]/R_beta, which is at least (1-e^{-R_beta})/R_beta and is also tight. We further show that all-or-nothing allocation policies cannot match these guarantees. These findings demonstrate that distributional stationarity strictly improves the fairness frontier, and that partial fulfillment is a necessary condition for attaining optimal fairness in online indivisible resource allocation.

math.OC↗

arXiv2023

Approximation Algorithms for Line Planning with Heterogeneous Fleets and Multiple Resource Constraints

This paper studies line planning for urban bus networks that face multiple resource limits such as budget, labor, and emission caps while using heterogeneous fleets. The objective is to maximize total reward from serving passengers by assigning buses to candidate routes subject to capacity and resource constraints. The reward parameters are general and can encode diverse user preferences and multi-modal system configurations. Prior work typically assumes single resource constraints and homogeneous fleets, and often relies on methods that lack theoretical guarantees or computational tractability. We develop the first approximation algorithms with provable guarantees for this setting. For the cost-free variant, a randomized rounding scheme attains the optimal ratio $1-1/e$ which is tight unless $P = NP$. Leveraging this base algorithm, we derive extensions for the general case with arbitrary cost vectors, obtaining constant-factor approximation guarantees. To support large-scale application, we adapt the base algorithm to ensure computational scalability while preserving rigorous theoretical guarantees. Experiments on Greater Boston transit data demonstrate that our approach achieves 95\% to 98\% of the linear programming relaxation bound, whereas Gurobi solver fails on considerably smaller instances. Our experiments further show that heterogeneous fleets significantly outperform homogeneous ones and that multi-resource optimization is required to avoid significant resource limit violations, thereby underscoring the importance of our framework.

math.OC↗

arXiv2021

Minimizing the total weighted pairwise connection time in network construction problems

It is required to find an optimal order of constructing the edges of a network so as to minimize the sum of the weighted connection times of relevant pairs of vertices. Construction can be performed anytime anywhere in the network, with a fixed overall construction speed. The problem is strongly NP-hard even on stars. We present polynomial algorithms for the problem on trees with a fixed number of leaves, and on general networks with a fixed number of relevant pairs.

cs.DS↗

arXiv2020

Tree Optimization Based Heuristics and Metaheuristics in Network Construction Problems

We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than its travel speed, so relocation times are negligible with respect to construction times. It is required to find a construction schedule that minimizes a non-decreasing function of the times when various connections of interest become operational. Most problems of this class are strongly NP-hard on general networks, but are often tree-efficient, that is, polynomially solvable on trees. We develop a generic local search heuristic approach and two metaheuristics (Iterated Local Search and Tabu Search) for solving tree-efficient network construction problems on general networks, and explore them computationally. Results of computational experiments indicate that the methods have excellent performance.

cs.AI↗