scholarly journals Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 993 ◽  
Author(s):  
Urmila Pyakurel ◽  
Hari Nandan Nath ◽  
Stephan Dempe ◽  
Tanka Nath Dhamala
Keyword(s):  
Road Network ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Evacuation Planning ◽  
Dynamic Flow ◽  
The Road ◽  
Flow Problems ◽  
Dynamic Flows ◽  
The Difference ◽  
Planning Problems

Contraflow technique has gained a considerable focus in evacuation planning research over the past several years. In this work, we design efficient algorithms to solve the maximum, lex-maximum, earliest arrival, and quickest dynamic flow problems having constant attributes and their generalizations with partial contraflow reconfiguration in the context of evacuation planning. The partial static contraflow problems, that are foundations to the dynamic flows, are also studied. Moreover, the contraflow model with inflow-dependent transit time on arcs is introduced. A strongly polynomial time algorithm to compute approximate solution of the quickest partial contraflow problem on two terminal networks is presented, which is substantiated by numerical computations considering Kathmandu road network as an evacuation network. Our results show that the quickest time to evacuate a flow of value 100,000 units is reduced by more than 42% using the partial contraflow technique, and the difference is more with the increase in the flow value. Moreover, the technique keeps the record of the portions of the road network not used by the evacuees.

scholarly journals Fair Allocation based on Diminishing Differences

2017 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Haris Aziz ◽  
Avinatan Hassidim
Keyword(s):  
School Choice ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Conservative Extension ◽  
Score Functions ◽  
Full Characterization ◽  
Proportional Allocation ◽  
The Difference ◽  
Natural Way

Ranking alternatives is a natural way for humans to explain their preferences. It is being used in many settings, such as school choice (NY, Boston), Course allocations, and the Israeli medical lottery. In some cases (such as the latter two), several ``items'' are given to each participant. Without having any information on the underlying cardinal utilities, arguing about fairness of allocation requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where a X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation if it exists. Using simulations, we show that with high probability, a necessarily-proportional allocation does not exist but a necessarily-DD-proportional allocation exists, and moreover, that allocation is proportional according to the underlying cardinal utilities.

scholarly journals Resilience-Driven Road Network Retrofit Optimization Subject to Tropical Cyclones Induced Roadside Tree Blowdown

2020 ◽  
Author(s):  
Fuyu Hu ◽  
Saini Yang ◽  
Russell G. Thompson
Keyword(s):  
Tropical Cyclones ◽  
Polynomial Time ◽  
Road Network ◽  
Road Networks ◽  
Hainan Island ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Economic Losses ◽  
Recovery Efficiency ◽  
Physical Damage

Abstract This article focuses on decision making for retrofit investment of road networks in order to alleviate severe consequences of roadside tree blowdown during tropical cyclones. The consequences include both the physical damage associated with roadside trees and the functional degradation associated with road networks. A trilevel, two-stage, and multiobjective stochastic mathematical model was developed to dispatch limited resources to retrofit the roadside trees of a road network. In the model, a new metric was designed to evaluate the performance of a road network; resilience was considered from robustness and recovery efficiency of a road network. The proposed model is at least a nondeterministic polynomial-time hardness (NP-hard) problem, which is unlikely to be solved by a polynomial time algorithm. Pareto-optimal solutions for this problem can be obtained by a proposed trilevel algorithm. The random forest method was employed to transform the trilevel algorithm into a single-level algorithm in order to decrease the computation burden. Roadside tree retrofit of a provincial highway network on Hainan Island, China was selected as a case area because it suffers severely from tropical cyclones every year, where there is an urgency to upgrade roadside trees against tropical cyclones. We found that roadside tree retrofit investment significantly alleviates the expected economic losses of roadside tree blowdown, at the same time that it promotes robustness and expected recovery efficiency of the road network.

scholarly journals Supply Chain Batching Problem with Identical Orders and Lifespan

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Shanlin Li ◽  
Maoqin Li ◽  
Hong Yan
Keyword(s):  
Dynamic Programming ◽  
Processing Time ◽  
Recursion Formula ◽  
Dynamic Programming Algorithm ◽  
Setup Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Programming Algorithm ◽  
Short Lifespan ◽  
The Difference

In the real world, there are a large number of supply chains that involve the short lifespan products. In this paper, we consider an integrated production and distribution batch scheduling problem on a single machine for the orders with a short lifespan, because it may be cheaper or faster to process and distribute orders in a batch than to process and distribute them individually. Assume that the orders have the identical processing time and come from the same location, and the batch setup time is a constant. The problem is to choose the number of batches and batch sizes to minimize the total delivery time without violating the order lifespan. We first give a backward dynamic programming algorithm, but it is not an actually polynomial-time algorithm. Then we propose a constant time partial dynamic programming algorithm by doing further research into the recursion formula in the algorithm. Further, using the difference characteristics of the optimal value function, a specific calculating formula to solve the problem with the setup time being integer times of the processing time is obtained.

scholarly journals The Complexity of Planning Problems With Simple Causal Graphs

2008 ◽  
Vol 31 ◽  
pp. 319-351 ◽  
Author(s):  
O. Gimenez ◽  
A. Jonsson
Keyword(s):  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Planning Problem ◽  
State Variables ◽  
Plan Generation ◽  
Binary State ◽  
Causal Graphs ◽  
Np Complete ◽  
Binary State Variables ◽  
Planning Problems

We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state variables and acyclic causal graphs. This implies that plan generation may be tractable even when a planning problem has an exponentially long minimal solution. We also prove that the problem of plan existence for planning problems with multi-valued variables and chain causal graphs is NP-hard. Finally, we show that plan existence for planning problems with binary state variables and polytree causal graphs is NP-complete.

scholarly journals On the complexity of the balanced vertex ordering problem

2007 ◽  
Vol Vol. 9 no. 1 (Graph and Algorithms) ◽  
Author(s):  
Jan Kára ◽  
Jan Kratochvil ◽  
David R. Wood
Keyword(s):  
Polynomial Time ◽  
Maximum Degree ◽  
Graph Drawing ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Np Hard ◽  
Vertex Ordering ◽  
The Difference ◽  
Balanced Ordering ◽  
Applied Math

Graphs and Algorithms International audience We consider the problem of finding a balanced ordering of the vertices of a graph. More precisely, we want to minimise the sum, taken over all vertices v, of the difference between the number of neighbours to the left and right of v. This problem, which has applications in graph drawing, was recently introduced by Biedl et al. [Discrete Applied Math. 148:27―48, 2005]. They proved that the problem is solvable in polynomial time for graphs with maximum degree three, but NP-hard for graphs with maximum degree six. One of our main results is to close the gap in these results, by proving NP-hardness for graphs with maximum degree four. Furthermore, we prove that the problem remains NP-hard for planar graphs with maximum degree four and for 5-regular graphs. On the other hand, we introduce a polynomial time algorithm that determines whetherthere is a vertex ordering with total imbalance smaller than a fixed constant, and a polynomial time algorithm that determines whether a given multigraph with even degrees has an 'almost balanced' ordering.

scholarly journals Fair Allocation with Diminishing Differences

2020 ◽  
Vol 67 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Avinatan Hassidim ◽  
Haris Aziz
Keyword(s):  
School Choice ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Conservative Extension ◽  
Score Functions ◽  
Full Characterization ◽  
Proportional Allocation ◽  
The Difference ◽  
Natural Way

Ranking alternatives is a natural way for humans to explain their preferences. It is used in many settings, such as school choice, course allocations and residency matches. Without having any information on the underlying cardinal utilities, arguing about the fairness of allocations requires extending the ordinal item ranking to ordinal bundle ranking. The most commonly used such extension is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if its score is better according to all additive score functions. SD is a very conservative extension, by which few allocations are necessarily fair while many allocations are possibly fair. We propose to make a natural assumption on the underlying cardinal utilities of the players, namely that the difference between two items at the top is larger than the difference between two items at the bottom. This assumption implies a preference extension which we call diminishing differences (DD), where X is preferred over Y if its score is better according to all additive score functions satisfying the DD assumption. We give a full characterization of allocations that are necessarily-proportional or possibly-proportional according to this assumption. Based on this characterization, we present a polynomial-time algorithm for finding a necessarily-DD-proportional allocation whenever it exists. Using simulations, we compare the various fairness criteria in terms of their probability of existence, and their probability of being fair by the underlying cardinal valuations. We find that necessary-DD-proportionality fares well in both measures. We also consider envy-freeness and Pareto optimality under diminishing-differences, as well as chore allocation under the analogous condition --- increasing-differences.

scholarly journals An elimination method for isolated meshes in a road network considering stroke edge feature

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0239828
Author(s):  
Chengming Li ◽  
Wei Wu ◽  
Pengda Wu ◽  
Jie Yin ◽  
Peipei Guo
Keyword(s):  
Road Network ◽  
Spatial Representation ◽  
Elimination Method ◽  
The Road ◽  
Road Map ◽  
Sample Data ◽  
Mesh Density ◽  
The Difference ◽  
Road Segments ◽  
Edge Feature

The road network is the skeletal element of topographic maps at different scales. In general, urban roads are connected by road segments, thus forming a series of road meshes. Mesh elimination is a key step in evaluating the importance of roads during the road network data management and a prerequisite to the implementation of continuous multiscale spatial representation of road networks. The existing mesh-based method is an advanced road elimination method whereby meshes with the largest density are sequentially selected and road segments with the least importance in each mesh are eliminated. However, the road connectivity and integrity may be destroyed in specific areas by this method because some eliminated road segments could be located in the middle of road strokes. Therefore, this paper proposed an elimination method for isolated meshes in a road network considering stroke edge feature. First, small meshes were identified by using mesh density thresholds, which can be obtained by the sample data statistical algorithm. Thereafter, the small meshes related to the edge segments of road strokes were taken out and defined as stroke edge meshes, and the remaining small meshes were defined as stroke non-edge meshes. Second, by computing the mesh density of all stroke edge meshes, the mesh with the largest density was selected as the starting mesh, and the least important edge segment in the mesh was eliminated. The difference between the existing mesh-based method and the proposed method is that the starting mesh is a stroke edge mesh, not any given small mesh, and the eliminated segment is just only one of edge segments of strokes not chosen from among all segments. Third, mesh elimination was implemented by iteratively processing the stroke edge meshes with the largest mesh density until all of them were eliminated and their mesh density exceeded the threshold. The stroke non-edge meshes were directly preserved. Finally, a 1:10,000 topographic road map of an area in Jiangsu Province of China was used for validation. The experimental results show that for all stroke non-edge meshes and 23% of the stroke edge meshes, compared to the mesh-based method, the road stroke connectivity and integrity of road strokes were better preserved by the proposed method, and the remaining 77% of the elimination results for the stroke edge meshes were the same under the two methods.

scholarly journals Equilibrium computation in resource allocation games

2021 ◽  
Author(s):  
Tobias Harks ◽  
Veerle Timmermans
Keyword(s):  
Resource Allocation ◽  
Polynomial Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Congestion Games ◽  
Congestion Game ◽  
Equilibrium Computation ◽  
The Difference ◽  
Price Functions ◽  
Resource Allocation Games

AbstractWe study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and player-specific affine cost functions, we devise the first polynomial time algorithm computing a pure Nash equilibrium. Our algorithm is combinatorial and computes the exact equilibrium assuming rational input. The idea is to compute an equilibrium for an associated integrally-splittable singleton congestion game in which the players can only split their demands in integral multiples of a common packet size. While integral games have been considered in the literature before, no polynomial time algorithm computing an equilibrium was known. Also for this class, we devise the first polynomial time algorithm and use it as a building block for our main algorithm. We then develop a polynomial time computable transformation mapping a multimarket Cournot competition game with firm-specific affine price functions and quadratic costs to an associated atomic splittable congestion game as described above. The transformation preserves equilibria in either game and, thus, leads – via our first algorithm – to a polynomial time algorithm computing Cournot equilibria. Finally, our analysis for integrally-splittable games implies new bounds on the difference between real and integral Cournot equilibria. The bounds can be seen as a generalization of the recent bounds for single market oligopolies obtained by Todd (Math Op Res 41(3):1125–1134 2016, 10.1287/moor.2015.0771).

L(2,1,1)-Labeling of Circular-Arc Graphs

2021 ◽  
Vol 13 (2) ◽  
pp. 537-544
Author(s):  
S. Amanathulla ◽  
B. Bera ◽  
M. Pal
Keyword(s):  
Circuit Design ◽  
Coding Theory ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Graph Labeling ◽  
Frequency Assignment ◽  
Circular Arc ◽  
X Ray Crystallography ◽  
The Difference ◽  
Circular Arc Graphs

Graph labeling problem has been broadly studied in recent past for its wide applications, in mobile communication system for frequency assignment, radar, circuit design, X-ray crystallography, coding theory, etc. An L211-labeling  (L211L) of a graph G = (V, E) is a function γ : V → Z∗ such that |γ(u) − γ(v)| ≥ 2, if d(u, v) = 1 and |γ(u) − γ(v)| ≥ 1, if  d(u, v) = 1 or 2, where  Z∗  be the set of non-negative integers and d(u, v) represents the distance between the nodes u and v. The L211L numbers of a graph G, are denoted by λ2,1,1(G) which is the difference between largest and smallest labels used in L211L. In this article, for circular-arc graph (CAG) G we have proved that λ2,1,1(G) ≤ 6∆ − 4, where ∆ represents the degree of the graph. Beside this we have designed a polynomial time algorithm to label a CAG satisfying the conditions of L211L. The time complexity of the algorithm is O(n∆2), where n is the number of nodes of the graph G.

scholarly journals Evaluating the UK takeaway food environment around secondary schools: comparison of different methods

2020 ◽  
Vol 79 (OCE2) ◽  
Author(s):  
Ayyoub K. Taher ◽  
Charlotte E L. Evans ◽  
Graham P Clarke
Keyword(s):  
Secondary Schools ◽  
Food Environment ◽  
Primary Schools ◽  
Road Network ◽  
Wilcoxon Test ◽  
Network Density ◽  
The Road ◽  
Straight Line ◽  
The Difference ◽  
The Uk

AbstractTakeaway shops are more clustered around secondary than primary schools and UK planning policies to limit takeaways show poor implementation against international examples and good practice statements. A major concern is that, worldwide, there are no standardised measures used to measure the food environment around homes, schools, work or any other facilities. This study aims to examine the differences in using different methods to evaluate the food environment particularly around secondary schools in the Avon region in the UK. Geographical Information System (GIS) was used to locate all schools and takeaways in the region and to measure the density and proximity scores, applying both road network and straight-line methods. In addition, the Hansen Index was used to measure the accessibility score of each schools to all takeaways in the region (not just the nearest). All of the nonparametric statistical analysis tests including Wilcoxon test, agreement (Kappa statistic) test and correlation test were carried out using Stata software version 15.0. It was observed that more than 50% of the schools had no takeaway shops within 200, 400, and 600 metres when the road network buffer was used. Statistical differences were observed between the road network and the straight-line methods. For example, the median of the difference between the straight-line and road network density within 1000 metres was 4.1 (CI 2.6, 5.9; P < 0.001). The median of the difference between the road network and straight-line proximity was 203.2 (CI 144.6, 261.9; P < 0.001). Also, the agreement between straight-line and road network densities within 800 (Kappa = 0.38) and 1000 (Kappa = 0.47) metres were fair and moderate, respectively. The agreement between both methods to measure the proximity was fair to moderate (Kappa = 0.40). In addition, the correlation results showed that both the straight-line and road network proximity were negatively correlated to the accessibility score measured. Our findings suggest that the 800 and 1000 metres road network density and proximity may be more appropriate to explore the real relationships between fast food accessibility and diet or health relationships. In addition, the Hansen index is another metric that may be used if the aim of the study is to consider multiple locations when calculating the accessibility score. The availability of best-practice methods would help to explore the food environment in a consistent way and therefore lead to the implementation of effective actions and policies targeting the food environments, particularly around secondary schools.

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