For two vertex clusters of a tree metric, we show that the sum of the average intracluster distances is always less than or equal to twice of the average intercluster distance. We show the feature in a more general fo...
详细信息
For two vertex clusters of a tree metric, we show that the sum of the average intracluster distances is always less than or equal to twice of the average intercluster distance. We show the feature in a more general form of weighted distance. This feature provides a 2-approximation algorithm for the minimum average intercluster distance spanning tree problem, which is a generalization of the minimum routing cost spanning tree or minimum average distance spanning tree problem. The results in this paper can be further generalized to more than two clusters. (c) 2006 Elsevier B.V. All rights reserved.
Multihop infrastructure wireless mesh networks offer increased reliability, coverage, and reduced equipment costs over their single-hop counterpart, wireless local area networks. Equipping wireless routers with multip...
详细信息
Multihop infrastructure wireless mesh networks offer increased reliability, coverage, and reduced equipment costs over their single-hop counterpart, wireless local area networks. Equipping wireless routers with multiple radios further improves the capacity by transmitting over multiple radios simultaneously using orthogonal. channels. Efficient channel assignment and routing is essential for throughput optimization of mesh clients. Efficient channel assignment schemes can greatly relieve the interference effect of close-by transmissions;effective routing schemes can alleviate potential congestion on any gateways to the Internet, thereby improving per-client throughput. Unlike previous heuristic approaches, we mathematically formulate the joint channel assignment and routing problem, taking into account the interference constraints, the number of channels in the network, and the number of radios available at each mesh router. We then use this formulation to develop a solution for our problem that optimizes the overall network throughput subject to fairness constraints on allocation of scarce wireless capacity among mobile clients. We show that the performance of our algorithms is within a constant factor of that of any optimal algorithm for the joint channel assignment and routing problem. Our evaluation demonstrates that our algorithm can effectively exploit the increased number of channels and radios, and it performs much better than the theoretical worst case bounds.
Suppose that we have a timetable of a round-robin tournament with a number of teams, and distances among their homes. The home-away assignment problem is to find a home-away assignment that minimizes the total traveli...
详细信息
Suppose that we have a timetable of a round-robin tournament with a number of teams, and distances among their homes. The home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance of the teams. We propose a formulation of the home-away assignment problem as an integer program, and a rounding algorithm based on Bertsimas, Teo and Vohra's dependent randomized rounding method [2]. Computational experiments show that our method quickly generates feasible solutions close to optimal.
We consider the problem of computing the minimum value pm taken by a polynomial p(x) of degree d over the standard simplex Delta. This is an NP-hard problem already for degree d = 2. For any integer k >= 1, by mini...
详细信息
We consider the problem of computing the minimum value pm taken by a polynomial p(x) of degree d over the standard simplex Delta. This is an NP-hard problem already for degree d = 2. For any integer k >= 1, by minimizing p(x) over the set of rational points in Delta with denominator k, one obtains a hierarchy of upper bounds p(Delta)(k) converging to p(min) as k --> infinity. These upper approximations are intimately linked to a hierarchy of lower bounds for p(min) constructed via polya's theorem about representations of positive forms on the simplex. Revisiting the proof of Polya's theorem allows us to give estimates on the quality of these upper and lower approximations for p(min). Moreover, we show that the bounds p(Delta)(k) yield a polynomial time approximation scheme for the minimization of polynomials of fixed degree d on the simplex, extending an earlier result of Bomze and De Klerk for degree d = 2. (C) 2006 Elsevier B.V. All rights reserved.
We present lower bounds for the vehicle routing problem (VRP) with and without split deliveries, improving the well known bound of Haimovich and Rinnooy Kan. These bounds are then utilized in a design of best-to-date ...
详细信息
We present lower bounds for the vehicle routing problem (VRP) with and without split deliveries, improving the well known bound of Haimovich and Rinnooy Kan. These bounds are then utilized in a design of best-to-date approximation algorithms. (c) 2006 Elsevier B.V. All rights reserved.
This paper considers the break minimization problem in sports timetabling. The problem is to find, under a given timetable of a round-robin tournament, a home-away assignment that minimizes the number of breaks, i.e.,...
详细信息
This paper considers the break minimization problem in sports timetabling. The problem is to find, under a given timetable of a round-robin tournament, a home-away assignment that minimizes the number of breaks, i.e., the number of occurrences of consecutive matches held either both at away or both at home for a team. We formulate the break minimization problem as MAX RES CUT and MAX 2SAT, and apply Goemans and Williamson's approximation algorithm using semidefinite programming. Computational experiments show that our approach quickly generates solutions of good approximation ratios. (c) 2004 Elsevier Ltd. All rights reserved.
In this paper, we present new algorithms for online multicast routing in ad hoc networks where nodes are energy-constrained. The objective is to maximize the total amount of multicast message data routed successfully ...
详细信息
In this paper, we present new algorithms for online multicast routing in ad hoc networks where nodes are energy-constrained. The objective is to maximize the total amount of multicast message data routed successfully over the network without any knowledge of future multicast request arrivals and generation rates. Specifically, we first propose an online algorithm for the problem based on an exponential function of energy utilization at each node. The competitive ratio of the proposed algorithm is analyzed if admission control of multicast requests is permitted. We then provide another online algorithm for the problem, which is based on minimizing transmission energy consumption for each multicast request and guaranteeing that the local network lifetime is no less than gamma times of the optimum, where gamma is constant with 0algorithms, in terms of network capacity, network lifetime, and transmission energy consumption for each multicast request. The experimental results clearly indicate that, for online multicast routing in ad hoc wireless networks, the network capacity is proportional to the network lifetime if the transmission energy consumption for each multicast request is at the same time minimized. This is in contrast to the implication by Kar et al. that the network lifetime is proportional to the network capacity when they considered the online unicast routing by devising an algorithm based on the exponential function of energy utilization at each node.
Next-generation Internet gateways are expected to deal with higher volume of network traffic and also perform more sophisticated tasks besides packet forwarding. As the scale-up approach does not escape from the trade...
详细信息
Next-generation Internet gateways are expected to deal with higher volume of network traffic and also perform more sophisticated tasks besides packet forwarding. As the scale-up approach does not escape from the tradeoff between functionality and performance, architectural improvements such as clustering become necessary in the design of future Internet gateways. In this paper, we investigate different clustering architectures for high-performance, feature-rich Internet gateways and formally define the optimization problem behind these architectures as Multiple Gateway Traffic-Distribution Problem, both in a discrete and a continuous form. In addition to proposing various algorithms that solve the problem exactly and approximately, we also develop an on-line, self-adjusting scheme based on the solution algorithms. The numerical results of simulation suggest that the proposed approximate solution algorithms are effective and efficient, and the derived adaptive scheme is able to make the best decision on traffic distribution when dealing with the dynamic nature of network traffic in practice. (c) 2006 Elsevier B.V. All rights reserved.
We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job J(j) is associated with an interval, I-j, which consists of up to t segments, for some t >=...
详细信息
We consider the problem of scheduling jobs that are given as groups of nonintersecting segments on the real line. Each job J(j) is associated with an interval, I-j, which consists of up to t segments, for some t >= 1, and a weight (profit), w(j);two jobs are in conflict if their intervals intersect. Such jobs show up in a wide range of applications, including the transmission of continuous-media data, allocation of linear resources ( e. g., bandwidth in linear processor arrays), and computational biology/geometry. The objective is to schedule a subset of nonconflicting jobs of maximum total weight. Our problem can be formulated as the problem of finding a maximum weight independent set in a t-interval graph ( the special case of t = 1 is an ordinary interval graph). We show that, for t = 2, this problem is APX-hard, even for highly restricted instances. Our main result is a 2t-approximation algorithm for general instances. This is based on a novel fractional version of the Local Ratio technique. One implication of this result is the first constant factor approximation for nonoverlapping alignment of genomic sequences. We also derive a bicriteria polynomial time approximation scheme for a restricted subclass of t-interval graphs.
暂无评论