Chia Wei Lee

A Dynamic Data Placement Strategy for Hadoop in Heterogeneous Environments

Abstract Cloud computing is a type of parallel distributed computing system that has become a frequently used computer application. MapReduce is an effective programming model used in cloud computing and large-scale data-parallel applications. Hadoop is an open-source implementation of the MapReduce model, and is usually used for data-intensive applications such as data mining and web indexing. The current Hadoop implementation assumes that every node in a cluster has the same computing capacity and that the tasks are data-local, which may increase extra overhead and reduce MapReduce performance. This paper proposes a data placement algorithm to resolve the unbalanced node workload problem. The proposed method can dynamically adapt and balance data stored in each node based on the computing capacity of each node in a heterogeneous Hadoop cluster. The proposed method can reduce data transfer time to achieve improved Hadoop performance. The experimental results show that the dynamic data placement policy can decrease the time of execution and improve Hadoop performance in a heterogeneous cluster.

Pancyclicity of Matching Composition Networks under the Conditional Fault Model

A graph G = (V, E) is said to be conditional k-edge-fault pancyclic if, after removing k faulty edges from G and provided that each node is incident to at least two fault-free edges, the resulting graph contains a cycle of every length from its girth to \V\ inclusive. In this paper, we sketch the common properties of a class of networks called Matching Composition Networks (MCNs), such that the conditional edge-fault pancyclicity of MCNs can be determined from the derived properties. We then apply our technical theorem to show that an m-dimensional hyper-Petersen network is conditional (2m 5)-edge-fault pancyclic.

{2,3}-Restricted connectivity of locally twisted cubes

Given a graph G and non-negative integer h, the h-restricted connectivity of G is the minimum cardinality of a set of nodes in G, if exists, whose deletion disconnects G and the degree of each node in every remaining component is at least h. The h-restricted connectivity is a generalization of the classical connectivity and can provide more accurate measures for the reliability or fault-tolerance of multiprocessor system. The n-dimensional locally twisted cubes, denoted by LTQ n , are a well-known network topology for building multiprocessor systems. In this paper, we first show that 2-restricted connectivity of the n-dimensional locally twisted cubes is 4 n - 8 for n ? 4 , and show that 3-restricted connectivity is equal to 8 n - 24 for n ? 5 .

Conditional Edge-Fault Hamiltonicity of Cartesian Product Graphs

A graph G is conditional k-edge-fault Hamiltonian if it remains Hamiltonian after deleting at most k edges and each vertex incident to at least two nonfaulty edges. A graph G is k-edge-fault Hamiltonian-connected if it remains Hamiltonian-connected after deleting at most k edges. This study shows that the conditional edge-fault Hamiltonicity of the Cartesian product network G x H can be efficiently evaluated given two graphs G and H that are edge-fault Hamilton-connected and conditional edge-fault Hamiltonian. This study uses the result to evaluate the conditional edge-fault Hamiltonicity of two multiprocessor systems, the generalized hypercubes and the nearest neighbor mesh hypercubes, both of which belong to Cartesian product networks.

Approximation Algorithms for the Star k-Hub Center Problem in Metric Graphs

Given a metric graph \(G=(V, E, w)\) and a center \(c\in V\), and an integer k, the Star k-Hub Center Problem is to find a depth-2 spanning tree T of G rooted by c such that c has exactly k children and the diameter of T is minimized. Those children of c in T are called hubs. The Star k-Hub Center Problem is NP-hard. (Liang, Operations Research Letters, 2013) proved that for any \(\epsilon >0\), it is NP-hard to approximate the Star k-Hub Center Problem to within a ratio \(1.25-\epsilon \). In the same paper, a 3.5-approximation algorithm was given for the Star k-Hub Center Problem. In this paper, we show that for any \(\epsilon > 0\), to approximate the Star k-Hub Center Problem to a ratio \(1.5 - \epsilon \) is NP-hard. Moreover, we give 2-approximation and \(\frac{5}{3}\)-approximation algorithms for the same problem.

Approximability and inapproximability of the star p-hub center problem with parameterized triangle inequality

Abstract A complete weighted graph G = ( V , E , w ) is called Δ β -metric, for some β ≥ 1 / 2 , if G satisfies the β -triangle inequality, i.e., w ( u , v ) ≤ β ⋅ ( w ( u , x ) + w ( x , v ) ) for all vertices u , v , x ∈ V . Given a Δ β -metric graph G = ( V , E , w ) and a center c ∈ V , and an integer p , the Δ β -Star p -Hub Center problem ( Δ β -S p HCP) is to find a depth-2 spanning tree T of G rooted at c such that c has exactly p children (also called hubs) and the diameter of T is minimized. In this paper, we study Δ β -S p HCP for all β ≥ 1 2 . We show that for any ϵ > 0 , to approximate the Δ β -S p HCP to a ratio g ( β ) − ϵ is NP-hard and give r ( β ) -approximation algorithms for the same problem where g ( β ) and r ( β ) are functions of β . A subclass of metric graphs is identified that Δ β -S p HCP is polynomial-time solvable. Moreover, some r ( β ) -approximation algorithms given in this paper meet approximation lower bounds.

On the Complexity of the Star p-hub Center Problem with Parameterized Triangle Inequality

A complete weighted graph \(G= (V, E, w)\) is called \(\varDelta _{\beta }\)-metric, for some \(\beta \ge 1/2\), if G satisfies the \(\beta \)-triangle inequality, i.e., \(w(u,v) \le \beta \cdot (w(u,x) + w(x,v))\) for all vertices \(u,v,x\in V\). Given a \(\varDelta _{\beta }\)-metric graph \(G=(V, E, w)\) and a center \(c\in V\), and an integer p, the \(\varDelta _{\beta }\)-Star p-Hub Center Problem (\(\varDelta _{\beta }\)-SpHCP) is to find a depth-2 spanning tree T of G rooted at c such that c has exactly p children and the diameter of T is minimized. The children of c in T are called hubs. For \(\beta = 1\), \(\varDelta _{\beta }\)-SpHCP is NP-hard. (Chen et al., COCOON 2016) proved that for any \(\varepsilon >0\), it is NP-hard to approximate the \(\varDelta _{\beta }\)-SpHCP to within a ratio \(1.5-\varepsilon \) for \(\beta = 1\). In the same paper, a \(\frac{5}{3}\)-approximation algorithm was given for \(\varDelta _{\beta }\)-SpHCP for \(\beta = 1\). In this paper, we study \(\varDelta _{\beta }\)-SpHCP for all \(\beta \ge \frac{1}{2}\). We show that for any \(\varepsilon > 0\), to approximate the \(\varDelta _{\beta }\)-SpHCP to a ratio \(g(\beta ) - \varepsilon \) is NP-hard and we give \(r(\beta )\)-approximation algorithms for the same problem where \(g(\beta )\) and \(r(\beta )\) are functions of \(\beta \). If \(\beta \le \frac{3 - \sqrt{3}}{2}\), we have \(r(\beta ) = g(\beta ) = 1\), i.e., \(\varDelta _{\beta }\)-SpHCP is polynomial time solvable. If \(\frac{3-\sqrt{3}}{2} < \beta \le \frac{2}{3}\), we have \(r(\beta ) = g(\beta ) = \frac{1 + 2\beta - 2\beta ^2}{4(1-\beta )}\). For \(\frac{2}{3} \le \beta \le 1\), \(r(\beta ) = \min \{\frac{1 + 2\beta - 2\beta ^2}{4(1-\beta )}, 1 + \frac{4\beta ^2}{5\beta +1}\}\). Moreover, for \(\beta \ge 1\), we have \(r(\beta ) = \min \{\beta + \frac{4\beta ^2- 2\beta }{2 + \beta }, 2\beta + 1\}\). For \(\beta \ge 2\), the approximability of the problem (i.e., upper and lower bound) is linear in \(\beta \).

Hamiltonicity of product networks with faulty elements

A graph G is k-fault Hamiltonian (resp. Hamiltonian-connected) if after deleting at most k vertices and/or edges from G, the resulting graph remains Hamiltonian (resp. Hamiltonian-connected). Let δ_i be the minimum degree of G_i for i=0, 1. Given (δ_i-2)-fault Hamiltonian and (δ_i-3)-fault Hamiltonian-connected graph G_i for i=0, 1 , this study shows that the Cartesian product network G₀ ×G₁ is (δ₀+δ₁-2) -fault Hamiltonian and (δ₀+δ₁-3)-fault Hamiltonian-connected. We then apply the result to determine the fault-tolerant Hamiltonicity and Hamiltonian-connectivity of two multiprocessor systems, namely the generalized hypercube and the nearest neighbor mesh hypercube, both of which belong to Cartesian product networks. This study also demonstrates that these results are worst-case optimal with respect to the number of faults tolerated.

Diagnosability of Component-Composition Graphs in the MM* Model

Diagnosability is an important metric for measuring the reliability of multiprocessor systems. This article adopts the MM* model and outlines the common properties of a wide class of interconnection networks, called component-composition graphs (CCGs), to determine their diagnosability by using their obtained properties. By applying the results to multiprocessor systems, the diagnosability of hypercube-like networks (including hypercubes, crossed cubes, Möbius cubes, twisted cubes, locally twisted cubes, generalized twisted cubes, and recursive circulants), star graphs, pancake graphs, bubble-sort graphs, and burnt pancake graphs, all of which belong to the class of CCGs, can also be computed.

Hamiltonicity of matching composition networks with conditional edge faults

In this paper, we sketch structure characterization of a class of networks, called Matching Composition Networks (MCNs), to establish necessary conditions for determining the conditional fault hamiltonicity. We then apply our result to n-dimensional restricted hypercube-like networks, including n-dimensional crossed cubes, and n-dimensional locally twisted cubes, to show that there exists a fault-free Hamiltonian cycle if there are at most 2n - 5 faulty edges in which each node is incident to at least two fault-free edges. We also demonstrate that our result is worst-case optimal with respect to the number of faulty edges tolerated.