We study some versions of the problem of finding the minimum size 2-connected subgraph. This problem is NP-hard (even on cubic planar graphs) and MAX SNP-hard. We show that the minimum 2-edge connected subgraph proble...
详细信息
We present approximation algorithms for two problems: Stochastic Boolean Function Evaluation (SBFE) and Stochastic Submodular Set Cover (SSSC). Our results for SBFE problems are obtained by reducing them to SSSC probl...
详细信息
Given an undirected graph G = (V, E) with non-negative costs on its edges, a root node r is an element of V, a set of demands D subset of or equal to V with demand v is an element of D wishing to route w(v) units of f...
详细信息
ISBN:
(纸本)3540228497
Given an undirected graph G = (V, E) with non-negative costs on its edges, a root node r is an element of V, a set of demands D subset of or equal to V with demand v is an element of D wishing to route w(v) units of flow (weight) to r, and a positive number k, the Capacitated Minimum Steiner Tree (CMStT) problem asks for a minimum Steiner tree, rooted at r, spanning the vertices in Dboolean OR{r} in which the sum of the vertex weights in every subtree hanging off r is at most k. When D = V, this problem is known as the Capacitated Minimum Spanning Tree (CMST) problem. Both CMStT and CMST problems are NP-hard. In this paper, we present approximation algorithms for these problems and several of their variants in network design. Our main results are the following. We give a (gammarho(ST) + 2)-approximation algorithm for the CMStT problem, where gamma is the inverse Steiner ratio and rho(ST) is the best achievable approximation ratio for the Steiner tree problem. Our ratio improves the current best ratio of 2rho(ST) + 2 for this problem. In particular, we obtain (gamma + 2)-approximation ratio for the CMST problem, which is an improvement over the current best ratio of 4 for this problem. For points in Euclidean and Rectilinear planes, our result translates into ratios of 3.1548 and 3.5, respectively. For instances in the plane, under the L, norm, with the vertices in D having uniform weights, we give a non-trivial (7/5rho(ST) + 3/2)-approximation algorithm for the CMStT problem. This translates into a ratio of 2.9 for the CMST problem with uniform vertex weights in the L-p metric plane. Our ratio of 2.9 solves the long standing open problem of obtaining a ratio any better than 3 for this case.
In this note, we shall consider constant factor approxi- mation algorithms for a variation of the discrete pierc- ing set problem for unit disks. Here a set of points P is given;the objective is to choose minimum numb...
详细信息
In this note, we shall consider constant factor approxi- mation algorithms for a variation of the discrete pierc- ing set problem for unit disks. Here a set of points P is given;the objective is to choose minimum number of points in P to pierce all the disks of unit radius centered at the points in P. We first propose a very simple al- gorithm that produces a 14-factor approximation result in O(n log n) time. Next, we improve the approxima- tion factor to 4 and then to 3. Both algorithms run in polynomial time.
In the Demand Strip Packing problem (DSP), we are given a time interval and a collection of tasks, each characterized by a processing time and a demand for a given resource (such as electricity, computational power, e...
详细信息
We present a (1-e)-approximation algorithms for maximum cardinality matchings in disk intersection graphs - all with near linear running time. We also present an estimation algorithm that returns (1 ± e)-approxim...
详细信息
Many recently designed approximation algorithms use a simple but apparently powerful idea. The algorithm is allowed to ask a trusted oracle for a small number (say O(log n)) bits of "advice." For instance, i...
详细信息
We study the prize-collecting version of the node-weighted Steiner tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for plan...
详细信息
We consider a tool- and setup-constrained short-term capacity allocation problem that arises in operational level planning at a semiconductor wafer fabrication facility. We formulate this problem as a degree-constrain...
详细信息
ISBN:
(纸本)3540204091
We consider a tool- and setup-constrained short-term capacity allocation problem that arises in operational level planning at a semiconductor wafer fabrication facility. We formulate this problem as a degree-constrained network flow problem on a bipartite graph. We show that the problem is NP-hard and propose the first constant factor (1/2) approximation algorithms. Experimental study demonstrates that, in practice, our algorithms give solutions that are on the average less than 1.5% away from the optimal solution in less than a second.
We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to schedule each job non-preemptively onto one of the machine...
详细信息
ISBN:
(纸本)9783959770187
We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to schedule each job non-preemptively onto one of the machines so as to minimize the makespan. In our problem, a job has its original processing time, which could be reduced by utilizing one of the resources. As resources are different, the amount of the time reduced for each job is different depending on the resource it uses. Once a resource is being used by one job, it can not be used simultaneously by any other job until this job is finished, hence the scheduler should take into account the job-To-machine assignment together with the resource-To-job assignment. We observe that, the classical unrelated machine scheduling problem is actually a special case of our problem when m = c, i.e., the number of resources equals the number of machines. Extending the techniques for the unrelated machine scheduling, we give a 2-approximation algorithm when both m and c are part of the input. We then consider two special cases for the problem, with m or c being a constant, and derive PTASes (Polynomial Time approximation Schemes) respectively. We also establish the relationship between the two parameters m and c, through which we are able to transform the PTAS for the case when m is constant to the case when c is a constant. The relationship between the two parameters reveals the structure within the problem, and may be of independent interest.
暂无评论