Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs

We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem. A cut graph of a graph G embedded on a surface S is a subgraph of G whose removal from S leaves a disk. We consider the problem of deciding whether an unweighted graph embedded on a surface of genus G has a cut graph of length at most a given value. We prove a time lower bound for this problem of n Ω( g log g ) conditionally to the ETH. In other words, the first n O(g) -time algorithm by Erickson and Har-Peled [SoCG 2002, Discr. Comput. Geom. 2004] is essentially optimal. We also prove that the problem is W[1]-hard when parameterized by the genus, answering a 17-year-old question of these authors. A multiway cut of an undirected graph G with t distinguished vertices, called terminals , is a set of edges whose removal disconnects all pairs of terminals. We consider the problem of deciding whether an unweighted graph G has a multiway cut of weight at most a given value. We prove a time lower bound for this problem of n Ω( gt + g 2 + t log ( g + t )) , conditionally to the ETH, for any choice of the genus g ≥ 0 of the graph and the number of terminals t ≥ 4. In other words, the algorithm by the second author [Algorithmica 2017] (for the more general multicut problem) is essentially optimal; this extends the lower bound by the third author [ICALP 2012] (for the planar case). Reductions to planar problems usually involve a gridlike structure. The main novel idea for our results is to understand what structures instead of grids are needed if we want to exploit optimally a certain value G of the genus.

Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling

Smoothed Particle Hydrodynamics (SPH) is a mesh-free numerical method that can simulate metal cutting problems efficiently. The thermal modeling of such processes with SPH, nevertheless, is not straightforward. The difficulty is rooted in the computationally demanding procedures regarding convergence properties and boundary treatments, both known as SPH Grand Challenges. This paper, therefore, intends to rectify these issues in SPH cutting models by proposing two improvements: (1) Implementing a higher-order Laplacian formulation to solve the heat equation more accurately. (2) Introducing a more realistic thermal boundary condition using a robust surface detection algorithm. We employ the proposed framework to simulate an orthogonal cutting process and validate the numerical results against the available experimental measurements.

Modeling and optimization of batch production based on layout and cutting problems under uncertainty

This paper presents a modeling and optimization of batch production based on layout, cutting and project scheduling problems by considering scenario planning. In order to solve the model, a novel genetic algorithm with an improvement procedure based on variable neighborhood search (VNS) is presented. Initially, the model is solved in small sizes using Lingo software and the combined genetic algorithm; then, the results are compared. Afterwards, the model is solved in large sizes by utilizing the proposed algorithm and simple genetic algorithm. The main findings of this paper show: 1) To prove the validity of the proposed method, a case study has been solved by employing the classical method (employing Lingo 11) and the results were compared to the ones developed by the proposed algorithm. Since the results are the same in both cases, the suggested algorithm is valid and able to achieve optimal and near-optimal solutions. 2) The combined genetic algorithm is more effective in achieving optimal boundaries and closer solutions in all cases compared to classical genetic algorithm. In other words, the main finding of this paper is a combined genetic algorithm to optimize batch production modeling problems, which is more efficient than the methods provided in the literature.

Steering, Knowledge and the Challenge of Governance Evaluation: The Case of National Health Service Governance and Reform in England

Drawing from “robust political economy” (RPE) literature, we address evaluative questions concerning governance effectiveness in the face of complex, cross-cutting problems. Central to RPE is the challenge of coordination, with its fundamental epistemological dimension requiring close attention to stakeholder knowledge about policy impacts. This focus contrasts with process-orientated analysis predominant in political science and public administration and enables holistic governance evaluation that draws from various, often demarcated, research fields. This is demonstrated through a focus on the evolution of health governance in England, particularly how diabetes services in England were affected by the 2012 Health and Social Care Act.