We present approximation algorithms for the unsplittable flow problem (UFP) in undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum Capacity. We focus on...
详细信息
We present approximation algorithms for the unsplittable flow problem (UFP) in undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum Capacity. We focus on the non-uniform capacity case in which the edge capacities can vary arbitrarily over the graph. Our results are: We obtain an O(Delta alpha(-1) log(2) n) approximation ratio for UFP, where n is the number of vertices, Delta is the maximum degree, and alpha is the expansion of the graph. Furthermore, if we specialize to the case where all edges have the same capacity, Our algorithm gives an O(Delta alpha(-1) log n) approximation. For certain strong constant-degree expanders considered by Frieze [17] we obtain an O(root log n) approximation for the uniform capacity case. For UFP on the line and the ring, we give the first constant-factor approximation algorithms. All of the above results improve if the maximum demand is bounded away from the minimum capacity. The above results either improve upon or are incomparable with previously known results for these problems. The main technique used for these results is randomized rounding followed by greedy alteration, and is inspired by the use of this idea in recent work.
We present a correction to the paper, "approximation algorithms for shop scheduling problems with minsum objective" (Journal of Scheduling 2002;5:287-305) by Queyranne and Sviridenko. This correction provide...
详细信息
We present a correction to the paper, "approximation algorithms for shop scheduling problems with minsum objective" (Journal of Scheduling 2002;5:287-305) by Queyranne and Sviridenko. This correction provides a correct derivation of its 2e rho approximation result.
Given a graph G = (V. E) a clique is a maximal subset of pairwise adjacent vertices of V of size at least 2. A clique transversal is a subset of vertices that intersects the vertex set of each clique of G. Finding a m...
详细信息
Given a graph G = (V. E) a clique is a maximal subset of pairwise adjacent vertices of V of size at least 2. A clique transversal is a subset of vertices that intersects the vertex set of each clique of G. Finding a minimum-cardinality clique transversal is NP-hard for the following classes: planar, line and bounded degree graphs. For line graphs we present a 3-approximation for the unweighted case and a 4-approximation for the weighted case with nonnegative weights;a inverted right perpendicular(G) + 1)/2inverted left perpendicular-approximation for bounded degree graphs and a 3-approximation for planar graphs. (C) 2015 Elsevier B.V. All rights reserved.
We study the covering-type k-violation linear program where at most k of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we prese...
详细信息
We study the covering-type k-violation linear program where at most k of the constraints can be violated. This problem is formulated as a mixed integer program and known to be strongly NP-hard. In this paper, we present a simple (k + 1)approximation algorithm using a natural LP relaxation. We also show that the integrality gap of the LP relaxation is k + 1. This implies we can not get better approximation algorithms when we use the LP-relaxation as a lower bound of the optimal value.
In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph G = (V, E;w;r) with length function w : E -> R+...
详细信息
In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph G = (V, E;w;r) with length function w : E -> R+ satisfying the triangle inequality, a fixed depot r is an element of V, and k vehicles having k nonuniform speeds lambda(1), lambda(2), ..., lambda(k), respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant delta > 0, we design a 20.8765(1 + delta)-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and 1/delta. (2) We present a (1 + Delta - 1/k)-approximation algorithm to solve the HCPP in cubic time, where Delta is the ratio of the largest vehicle speed to the smallest one.
This work deals with the continuous time lot-sizing inventory problem when demand and costs are time-dependent. We adapt a cost balancing technique developed for the periodic-review version of our problem to the conti...
详细信息
This work deals with the continuous time lot-sizing inventory problem when demand and costs are time-dependent. We adapt a cost balancing technique developed for the periodic-review version of our problem to the continuous-review framework. We prove that the solution obtained costs at most twice the cost of an optimal solution. We study the numerical complexity of the algorithm and generalize the policy to several important extensions while preserving its performance guarantee of two. Finally, we propose a modified version of our algorithm for the lot-sizing model with some restricted settings that improves the worst-case bound. (C) 2013 Elsevier B.V. All rights reserved.
One of the main goals in the analysis of microarray data is to identify groups of genes and groups of experimental conditions (including environments, individuals, and tissues) that exhibit similar expression patterns...
详细信息
One of the main goals in the analysis of microarray data is to identify groups of genes and groups of experimental conditions (including environments, individuals, and tissues) that exhibit similar expression patterns. This is the so-called biclustering problem. In this paper, we consider two variations of the biclustering problem: the consensus submatrix problem and the bottleneck submatrix problem. The input of the problems contains an m x n matrix A and integers l and k. The consensus submatrix problem is to find an l x k submatrix with l < m and k < n and a consensus vector such that the sum of distances between the rows in the submatrix and the consensus vector is minimized. The bottleneck submatrix problem is to find an l x k submatrix with l < m and k < n, an integer d and a center vector such that the distance between every row in the submatrix and the vector is at most d and d is minimized. We show that both problems are NP-hard and give randomized approximation algorithms for special cases of the two problems. Using standard techniques, we can derandomize the algorithms to get polynomial time approximation schemes for the two problems. To the best of our knowledge, this is the first time that approximation algorithms with guaranteed ratios are presented for microarray data analysis.
In this paper,we address the problem of constructing a Steiner tree in the Euclidean plane R^(2)using stock pieces of materials with fixed length,which is modelled as *** a set X={r_(1),r_(2)…,r_(n)}of n terminals in...
详细信息
In this paper,we address the problem of constructing a Steiner tree in the Euclidean plane R^(2)using stock pieces of materials with fixed length,which is modelled as *** a set X={r_(1),r_(2)…,r_(n)}of n terminals in R^(2)and some stock pieces of materials with fixed length L,we are asked to construct a Steiner tree T interconnecting all terminals in X,and each edge in T must be constructed by a part of that stock piece of *** objective is to minimize the cost of constructing such a Steiner tree T,where the cost includes three components,(1)The cost of Steiner points needed in T;(2)The construction cost of constructing all edges in T and(3)The cost of stock pieces of such materials used to construct all edges in *** can obtain two main results.(1)Using techniques of constructing a Euclidean minimum spanning tree on the set X and a strategy of solving the bin-packing problem,we present a simple 4-approximation algorithm in time O(n log n)to solve this new problem;(2)Using techniques of computational geometry to solve two nonlinear mathematical programming to obtain a key Lemma 8 and using other strategy of solving the bin-packing problem,we design a 3-approximation algorithm in time O(n^(3))to resolve this new problem.
The ring loading problem and its variants have been extensively studied in the last fifteen years, under the assumption that all requests have to be satisfied. However, in many practical cases, one may wish to reject ...
详细信息
The ring loading problem and its variants have been extensively studied in the last fifteen years, under the assumption that all requests have to be satisfied. However, in many practical cases, one may wish to reject some requests, which results in a penalty cost. We introduce the ring loading problem with penalty cost, which generalizes the well-known ring loading problem (Schrijver et al., 1999 [14]). We prove that this problem is NP-hard even if the demand can be split, and design a 1.58-approximation algorithm for the integer demand splittable case and a (1.58 + epsilon)-approximation algorithm for the demand unsplittable case, for any given number epsilon > 0. (C) 2013 Elsevier B.V. All rights reserved.
We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimi...
详细信息
We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects so as to minimize the average data-access cost. We introduce the data placement problem to model this problem. We have a set of caches F, a set of clients D, and a set of data objects O. Each cache i can store at most u(i) data objects. Each client j is an element of D has demand d(j) for a specific data object o(j) is an element of O and has to be assigned to a cache that stores that object. Storing an object o in cache i incurs a storage cost of f(i)(o), and assigning client j to cache i incurs an access cost of d(j)c(ij). The goal is to find a placement of the data objects to caches respecting the capacity constraints, and an assignment of clients to caches so as to minimize the total storage and client access costs. We present a 10-approximation algorithm for this problem. Our algorithm is based on rounding an optimal solution to a natural linear-programming relaxation of the problem. One of the main technical challenges encountered during rounding is to preserve the cache capacities while incurring only a constant-factor increase in the solution cost. We also introduce the connected data placement problem to capture settings where write-requests are also issued for data objects, so that one requires a mechanism to maintain consistency of data. We model this by requiring that all caches containing a given object be connected by a Steiner tree to a root for that object, which issues a multicast message upon a write to (any copy of) that object. The total cost now includes the cost of these Steiner trees. We devise a 14-approximation algorithm for this problem. We show that our algorithms can be adapted to handle two variants of the problem: (a) a k-median variant, where there is a specified bound on the number of caches that may contain a given object, and (b) a ge
暂无评论