We consider the problem of political redistricting: given the locations of people in a geographical area (e.g. a US state), the goal is to decompose the area into subareas, called districts, so that the populations of...
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ISBN:
(纸本)9781450358897
We consider the problem of political redistricting: given the locations of people in a geographical area (e.g. a US state), the goal is to decompose the area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are "compact" and "contiguous," to use the terms referred to in most US state constitutions and/or US Supreme Court rulings. We study a method that outputs a solution in which each district is the intersection of a convex polygon with the geographical area. The average number of sides per polygon is less than six. The polygons tend to be quite compact. Every two districts differ in population by at most one (so we call the solution balanced). In fact, the solution is a centroidal power diagram: each polygon has an associated center in R-3 such that the projection of the center onto the plane z = 0 is the centroid of the locations of people assigned to the polygon, and for each person assigned to that polygon, the polygon's center is closest among all centers. The polygons are convex because they are the intersections of 3D Voronoi cells with the plane. The solution is, in a well-defined sense, a locally optimal solution to the problem of choosing centers in the plane and choosing an assignment of people to those 2-d centers so as to minimize the sum of squared distances subject to the assignment being balanced. A practical problem with this approach is that, in real-world redistricting, exact locations of people are unknown. Instead, the input consists of polygons (census blocks) and associated populations. A real redistricting must not split census blocks. We therefore propose a second phase that perturbs the solution slightly so it does not split census blocks. In our experiments, the second phase achieves this while preserving perfect population balance. The district polygons are no longer convex at the fine scale because their boundaries must follow the boundaries of census blocks, but at a c
In Formal Concept Analysis, stability is an important utility measure to rank concepts. However, computation of stability is considered to be a hard problem. Efficient algorithms having good bounds to estimate stabili...
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ISBN:
(纸本)9789811082375;9789811082368
In Formal Concept Analysis, stability is an important utility measure to rank concepts. However, computation of stability is considered to be a hard problem. Efficient algorithms having good bounds to estimate stability holds promise. In this paper, an effective graph-based technique is proposed to estimate stability. Our estimation algorithm has a polynomial time complexity of O(vertical bar A vertical bar(2)) where vertical bar A vertical bar is the number of vertices.
In real Web applications, CoSimRank has been proposed as a powerful measure of node-pair similarity based on graph topologies. However, existing work on CoSimRank is restricted to static graphs. When the graph is upda...
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ISBN:
(纸本)9781450356398
In real Web applications, CoSimRank has been proposed as a powerful measure of node-pair similarity based on graph topologies. However, existing work on CoSimRank is restricted to static graphs. When the graph is updated with new edges arriving over time, it is cost-inhibitive to recompute all CoSimRank scores from scratch, which is impractical. In this study, we propose a fast dynamic scheme, D-CoSim, for accurate CoSimRank search over evolving graphs. Based on D-CoSim, we also propose a fast scheme, F-CoSim, that greatly accelerates CoSimRank search over static graphs. Our theoretical analysis shows that D-CoSim and F-CoSim guarantee the exactness of CoSimRank scores. On the static graph G, to efficiently retrieve CoSimRank scores S, F-CoSim is based on three ideas: (i) It first finds a "spanning polytree" T over G. (ii) On T, a fast algorithm is designed to compute the CoSimRank scores S(T) over the "spanning polytree" T. (iii) On G, D-CoSim is employed to compute the changes of S(T) in response to the delta graph (G circle minus T). Experimental evaluations verify the superiority of D-CoSim over evolving graphs, and the fast speedup of F-CoSim on large-scale static graphs against its competitors, without any loss of accuracy.
Computing connected components is an important graph algorithm that is used, for example, in medicine, image processing, and biochemistry. This paper presents a fast connected-components implementation for GPUs called...
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ISBN:
(纸本)9781450357852
Computing connected components is an important graph algorithm that is used, for example, in medicine, image processing, and biochemistry. This paper presents a fast connected-components implementation for GPUs called ECL-CC. It builds upon the best features of prior algorithms and augments them with GPU-specific optimizations. For example, it incorporates a parallelism-friendly version of pointer jumping to speed up union-find operations and uses several compute kernels to exploit the multiple levels of hardware parallelism. The resulting CUDA code is asynchronous and lock free, employs load balancing, visits each edge exactly once, and only processes edges in one direction. It is 1.8 times faster on average than the fastest prior GPU implementation running on a Titan X and faster on most of the eighteen real-world and synthetic graphs we tested.
For a finite undirected graph G = (V, E) and a positive integer k >= 1, an edge set M subset of E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been ...
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ISBN:
(纸本)9781450365390
For a finite undirected graph G = (V, E) and a positive integer k >= 1, an edge set M subset of E is a distance-k matching if the pairwise distance of edges in M is at least k in G. The special case k = 2 has been studied under the name maximum induced matching (MIM for short), i.e., a maximum matching which forms an induced subgraph in G. MIM arises in many applications, such as artificial intelligence, game theory, computer networks, VLSI design and marriage problems. In this paper, we design an O(n(2)) solution for finding MIM in permutation graphs based on a dynamic programming method on edges with the aid of the sweep line technique. Our result is better than the best known algorithm.
Reachability query with label constraint in an attribute graph is one of the most fundamental and important operations in semantic network analysis. However, ever-growing graph size has resulted in intractable reachab...
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Reachability query with label constraint in an attribute graph is one of the most fundamental and important operations in semantic network analysis. However, ever-growing graph size has resulted in intractable reachability problems on single machines. This work aims to devise efficient solutions for the reachability with label constraint problem in an attribute graph in a distributed environment. We focus on two issues in distributed processingdata locality and workload balancingsince data locality reduces communication overhead and workload balancing improves the efficiency of cluster use. We propose three novel techniques to address the two issues: (1) a partition replication method that improves data locality while conserving community property, (2) a workload-prediction method that accurately predicts machine workloads for a given quer, and (3) a workload balancing method that uses these predictions to shift partial workloads among machines to produce a balanced workload. Experimental results suggest that these techniques significantly improve performance and reduce total execution time by 40%.
this paper is regarding the lack of semantic factor in recommendation systems and describes the different recommendation techniques that are being employed in the current e-commerce website. Recommendation system can ...
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ISBN:
(纸本)9781509015603
this paper is regarding the lack of semantic factor in recommendation systems and describes the different recommendation techniques that are being employed in the current e-commerce website. Recommendation system can be broadly classified into three categories: content-based, collaborative, and hybrid recommendation approaches. Content based systems consider the properties of the items to be recommended. For instance, if a Amazon user has purchased many romantic novels, then content based recommendation system recommends novels in the database as having the "romantic" genre. Collaborative filtering systems recommend items based on similarity measures between like minded users and/or items. The items recommended to a user are those preferred by similar users. This paper also emphasizes the need for semantics in current recommendation system to recommend products accurately. This also describes various limitations that are present in the current recommendation methods and suggests possible solutions that can improve current recommendation system used in e-commerce websites. It also includes a survey on popular e-commerce websites such as Amazon, Ebay, Flipkart Snapdeal and Paytm by rating them on different parameters and doing their comparative analyses This paper also focuses on how graph algorithm can be used to improve recommendation in e-commerce websites. The proposed system compares *** recommendation of images with the proposed method. The method incorporates semantic recommendation using overlap technique based in graph.
The recent years have witnessed the remarkable expansion of publicly available biological data in the related research fields. Many researches in these fields often require massive data to be analyzed by utilizing hig...
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ISBN:
(纸本)9781509063185
The recent years have witnessed the remarkable expansion of publicly available biological data in the related research fields. Many researches in these fields often require massive data to be analyzed by utilizing high-throughput sequencing technologies. However, it is very challenging to interpret the data efficiently due to it high complexity. This paper introduces two new graph algorithms which aim to improve the efficiency of the existing methods for biological network data interpretation. In particular, the algorithms focus on the problem of how to simplify gene regulatory networks so that many existing algorithms can efficiently discover important connected components of a biological system in their own context as many times as they need. The performance of the proposed algorithms is compared with each other with gene expression data of glioblastoma brain tumor cancer.
This paper studies a variant of the graph partitioning problem, called the evacuation planning problem, which asks us to partition a target area, represented by a graph, into several regions so that each region contai...
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This paper studies a variant of the graph partitioning problem, called the evacuation planning problem, which asks us to partition a target area, represented by a graph, into several regions so that each region contains exactly one shelter. Each region must be convex to reduce intersections of evacuation routes, the distance between each point to a shelter must be bounded so that inhabitants can quickly evacuate from a disaster, and the number of inhabitants assigned to each shelter must not exceed the capacity of the shelter. This paper formulates the convexity of connected components as a spanning shortest path forest for general graphs, and proposes a novel algorithm to tackle this multi-objective optimization problem. The algorithm not only obtains a single partition but also enumerates all partitions simultaneously satisfying the above complex constraints, which is difficult to be treated by existing algorithms, using zero-suppressed binary decision diagrams (ZDDs) as a compressed expression. The efficiency of the proposed algorithm is confirmed by the experiments using real-world map data. The results of the experiments show that the proposed algorithm can obtain hundreds of millions of partitions satisfying all the constraints for input graphs with a hundred of edges in a few minutes.
In this paper, we propose and analyze a simple local algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwardin...
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In this paper, we propose and analyze a simple local algorithm to balance a tree. The motivation comes from live distributed streaming systems in which a source diffuses a content to peers via a tree, a node forwarding the data to its children. Such systems are subject to a high churn, peers frequently joining and leaving the system. It is thus crucial to be able to repair the diffusion tree to allow an efficient data distribution. In particular, due to bandwidth limitations, an efficient diffusion tree must ensure that node degrees are bounded. Moreover, to minimize the delay of the streaming, the depth of the diffusion tree must also be controlled. We propose here a simple distributed repair algorithm in which each node carries out local operations based on its degree and on the subtree sizes of its children. In a synchronous setting, we first prove that starting from any n-node tree our process converges to a balanced binary tree in O(n(2)) rounds. We then describe a more restrictive model, adding a small extra information to each node, under which we adapt our algorithm to converge in circle minus(n log n) rounds. (C) 2017 Elsevier B.V. All rights reserved.
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