A general framework for handling commitment in online throughput maximization

We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least $1+\varepsilon$ times its processing time, for some $\varepsilon>0$. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of $O(1/\varepsilon)$ is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a $\delta$-fraction of its size, we prove a competitive ratio of $O(\varepsilon/((\varepsilon-\delta)\delta^2))$, for $0<\delta<\varepsilon$. When a provider must commit upon starting a job, our bound is $O(1/\varepsilon^2)$. Finally, we observe that for scheduling with commitment the restriction to the `unweighted' throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms

A general framework for handling commitment in online throughput maximization

We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least 1+epsilon times its processing time, for some epsilon>0. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of O(1/epsilon) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job's slack becomes less than a delta-fraction of its size, we prove a competitive ratio of O(epsilon/((epsilon-delta)delta(2))), for 0<delta<epsilon. When a provider must commit upon starting a job, our bound is O(1/epsilon(2)). Finally, we observe that for scheduling with commitment the restriction to the unweighted throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms

Integer Programming and Combinatorial Optimization [electronic resource] : 20th International Conference, IPCO 2019, Ann Arbor, MI, USA, May 22-24, 2019, Proceedings /

This book constitutes the refereed proceedings of the 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019, held in Ann Arbor, MI, USA, in May 2019. The 33 full versions of extended abstracts presented were carefully reviewed and selected from 114 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas.Identically Self-Blocking Clutters -- Min-Max Correlation Clustering via -- Strong Mixed-Integer Programming Formulations for Trained Neural -- Extended Formulations from Communication Protocols in Output-Efficient -- Sub-Symmetry-Breaking Inequalities for ILP with Structured Symmetry -- Intersection Cuts for Polynomial Optimization -- Fixed-Order Scheduling on Parallel Machines -- Online Submodular Maximization: Beating 1/2 Made Simple -- Improving the Integrality Gap for Multiway Cut -- nell 1-sparsity Approximation Bounds for Packing Integer Programs -- A General Framework for Handling Commitment in Online Throughput Maximization -- Lower Bounds and A New Exact Approach for the Bilevel Knapsack with Interdiction Constraints -- On Friedmann's Subexponential Lower Bound for Zadeh's Pivot Rule -- Tight Approximation Ratio for Minimum Maximal Matching -- Integer Programming and Incidence Treedepth -- A Bundle Approach for SDPs with Exact Subgraph Constraints -- Dynamic Flows with Adaptive Route Choice -- The Markovian Price of Information -- On Perturbation Spaces of Minimal Valid Functions: Inverse Semigroup Theory and Equivariant Decomposition Theorem -- On Compact Representations of Voronoi Cells of Lattices -- An Efficient Characterization of Submodular Spanning Tree Games -- The Asymmetric Traveling Salesman Path LP Has Constant Integrality Ratio -- Approximate Multi-Matroid Intersection via Iterative Refinement -- An Exact Algorithm for Robust Influence Maximization -- A New Contraction Technique with Applications to Congruency-Constrained Cuts -- Sparsity of Integer Solutions in the Average Case -- A Generic Exact Solver for Vehicle Routing and Related Problems -- Earliest Arrival Transshipments in Networks With Multiple Sinks -- Intersection Cuts for Factorable MINLP -- Linear Programming Using Limited-Precision Oracles -- Computing the Nucleolus of Weighted Cooperative Matching Games in Polynomial Time -- Breaking Symmetries to Rescue SoS: The Case of Makespan Scheduling -- Random Projections for Quadratic Programs over a Euclidean Ball.This book constitutes the refereed proceedings of the 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019, held in Ann Arbor, MI, USA, in May 2019. The 33 full versions of extended abstracts presented were carefully reviewed and selected from 114 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas