scholarly journals Graphical Cake Cutting via Maximin Share

2021 ◽  
Author(s):  
Edith Elkind ◽  
Erel Segal-Halevi ◽  
Warut Suksompong
Keyword(s):  
Undirected Graph ◽  
Road Networks ◽  
Cake Cutting ◽  
General Graphs

We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed; however, in the latter case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.

scholarly journals Graphs with maximal irregularity

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1315-1322 ◽  
Author(s):  
Hosam Abdo ◽  
Nathann Cohen ◽  
Darko Dimitrov
Keyword(s):  
Upper Bound ◽  
Undirected Graph ◽  
Graph Invariant ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Chemical Graph Theory ◽  
Degree Of A Vertex ◽  
Maximal Vertex ◽  
Vertex Degrees ◽  
General Graphs

Albertson [3] has defined the P irregularity of a simple undirected graph G = (V,E) as irr(G) =?uv?E |dG(u)- dG(v)|, where dG(u) denotes the degree of a vertex u ? V. Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [12]. For general graphs with n vertices, Albertson has obtained an asymptotically tight upper bound on the irregularity of 4n3/27: Here, by exploiting a different approach than in [3], we show that for general graphs with n vertices the upper bound ?n/3? ?2n/3? (?2n/3? -1) is sharp. We also present lower bounds on the maximal irregularity of graphs with fixed minimal and/or maximal vertex degrees, and consider an approximate computation of the irregularity of a graph.

Continuous K Nearest Neighbor Queries of Moving Objects in Road Networks

2010 ◽  
Vol 33 (8) ◽  
pp. 1396-1404 ◽  
Author(s):  
Liang ZHAO ◽  
Luo CHEN ◽  
Ning JING ◽  
Wei LIAO
Keyword(s):  
Moving Objects ◽  
Nearest Neighbor ◽  
Road Networks ◽  
Nearest Neighbor Queries

NNlists-based k-path nearest neighbor query in road networks

2010 ◽  
Vol 30 (7) ◽  
pp. 1947-1949
Author(s):  
Bao-wen WANG ◽  
Jing-jing HAN ◽  
Zi-jun CHEN ◽  
Wen-yuan LIU
Keyword(s):  
Nearest Neighbor ◽  
Road Networks ◽  
Nearest Neighbor Query

Modeling Phase Changes of Road Networks

2009 ◽  
Author(s):  
Arthur Huang ◽  
David Matthew Levinson
Keyword(s):  
Road Networks ◽  
Phase Changes

scholarly journals On the star forest polytope for trees and cycles

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1773
Author(s):  
Meziane Aider ◽  
Lamia Aoudia ◽  
Mourad Baïou ◽  
A. Ridha Mahjoub ◽  
Viet Hung Nguyen
Keyword(s):  
Undirected Graph ◽  
Dominating Set ◽  
Discrete Math ◽  
Complete Characterization ◽  
Facial Structure ◽  
Maximum Weight ◽  
Single Node ◽  
End Node ◽  
Vertex Disjoint

Let G = (V, E) be an undirected graph where the edges in E have non-negative weights. A star in G is either a single node of G or a subgraph of G where all the edges share one common end-node. A star forest is a collection of vertex-disjoint stars in G. The weight of a star forest is the sum of the weights of its edges. This paper deals with the problem of finding a Maximum Weight Spanning Star Forest (MWSFP) in G. This problem is NP-hard but can be solved in polynomial time when G is a cactus [Nguyen, Discrete Math. Algorithms App. 7 (2015) 1550018]. In this paper, we present a polyhedral investigation of the MWSFP. More precisely, we study the facial structure of the star forest polytope, denoted by SFP(G), which is the convex hull of the incidence vectors of the star forests of G. First, we prove several basic properties of SFP(G) and propose an integer programming formulation for MWSFP. Then, we give a class of facet-defining inequalities, called M-tree inequalities, for SFP(G). We show that for the case when G is a tree, the M-tree and the nonnegativity inequalities give a complete characterization of SFP(G). Finally, based on the description of the dominating set polytope on cycles given by Bouchakour et al. [Eur. J. Combin. 29 (2008) 652–661], we give a complete linear description of SFP(G) when G is a cycle.

scholarly journals Evaluating the Safety Risk of Rural Roadsides Using a Bayesian Network Method

2019 ◽  
Vol 16 (7) ◽  
pp. 1166 ◽  
Author(s):  
Tianpei Tang ◽  
Senlai Zhu ◽  
Yuntao Guo ◽  
Xizhao Zhou ◽  
Yang Cao
Keyword(s):  
Bayesian Network ◽  
Low Cost ◽  
Road Networks ◽  
Access Point ◽  
Safety Risk ◽  
Crash Data ◽  
Risk Levels ◽  
The Road ◽  
Run Off ◽  
Point Density

Evaluating the safety risk of rural roadsides is critical for achieving reasonable allocation of a limited budget and avoiding excessive installation of safety facilities. To assess the safety risk of rural roadsides when the crash data are unavailable or missing, this study proposed a Bayesian Network (BN) method that uses the experts’ judgments on the conditional probability of different safety risk factors to evaluate the safety risk of rural roadsides. Eight factors were considered, including seven factors identified in the literature and a new factor named access point density. To validate the effectiveness of the proposed method, a case study was conducted using 19.42 km long road networks in the rural area of Nantong, China. By comparing the results of the proposed method and run-off-road (ROR) crash data from 2015–2016 in the study area, the road segments with higher safety risk levels identified by the proposed method were found to be statistically significantly correlated with higher crash severity based on the crash data. In addition, by comparing the respective results evaluated by eight factors and seven factors (a new factor removed), we also found that access point density significantly contributed to the safety risk of rural roadsides. These results show that the proposed method can be considered as a low-cost solution to evaluating the safety risk of rural roadsides with relatively high accuracy, especially for areas with large rural road networks and incomplete ROR crash data due to budget limitation, human errors, negligence, or inconsistent crash recordings.

scholarly journals Modeling of Emergency Supply Scheduling Problem Based on Reliability and Its Solution Algorithm under Variable Road Network after Sudden-Onset Disasters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Tinggui Chen ◽  
Shiwen Wu ◽  
Jianjun Yang ◽  
Guodong Cong ◽  
Gongfa Li
Keyword(s):  
Road Network ◽  
Road Networks ◽  
Sudden Onset ◽  
The Road ◽  
Bee Colony ◽  
Proposed Model ◽  
Effectiveness And Efficiency ◽  
In Transit ◽  
Emergency Supply

It is common that many roads in disaster areas are damaged and obstructed after sudden-onset disasters. The phenomenon often comes with escalated traffic deterioration that raises the time and cost of emergency supply scheduling. Fortunately, repairing road network will shorten the time of in-transit distribution. In this paper, according to the characteristics of emergency supplies distribution, an emergency supply scheduling model based on multiple warehouses and stricken locations is constructed to deal with the failure of part of road networks in the early postdisaster phase. The detailed process is as follows. When part of the road networks fail, we firstly determine whether to repair the damaged road networks, and then a model of reliable emergency supply scheduling based on bi-level programming is proposed. Subsequently, an improved artificial bee colony algorithm is presented to solve the problem mentioned above. Finally, through a case study, the effectiveness and efficiency of the proposed model and algorithm are verified.

scholarly journals Exploiting Data Analytics and Deep Learning Systems to Support Pavement Maintenance Decisions

2021 ◽  
Vol 11 (6) ◽  
pp. 2458
Author(s):  
Ronald Roberts ◽  
Laura Inzerillo ◽  
Gaetano Di Mino
Keyword(s):  
Deep Learning ◽  
Management Practices ◽  
Prediction Models ◽  
Road Networks ◽  
Pavement Management ◽  
Efficient Operation ◽  
Pavement Maintenance ◽  
Goods And Services ◽  
Maintenance Decisions ◽  
Computational Systems

Road networks are critical infrastructures within any region and it is imperative to maintain their conditions for safe and effective movement of goods and services. Road Management, therefore, plays a key role to ensure consistent efficient operation. However, significant resources are required to perform necessary maintenance activities to achieve and maintain high levels of service. Pavement maintenance can typically be very expensive and decisions are needed concerning planning and prioritizing interventions. Data are key towards enabling adequate maintenance planning but in many instances, there is limited available information especially in small or under-resourced urban road authorities. This study develops a roadmap to help these authorities by using flexible data analysis and deep learning computational systems to highlight important factors within road networks, which are used to construct models that can help predict future intervention timelines. A case study in Palermo, Italy was successfully developed to demonstrate how the techniques could be applied to perform appropriate feature selection and prediction models based on limited data sources. The workflow provides a pathway towards more effective pavement maintenance management practices using techniques that can be readily adapted based on different environments. This takes another step towards automating these practices within the pavement management system.

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