45415063
Np-hardness proof and an approximation algorithm for the minimum vertex ranking spanning tree problem
The minimum vertex ranking spanning tree problem (MVRST) is to find a spanning tree of G whose vertex ranking is minimum. In this paper, we show that MVRST is NP-hard. To prove this, we polynomially reduce the 3-dimensional matching problem to MVRST. Moreover, we present a (⌈Ds/2⌉ + 1)/(⌊log2(Ds + 1)⌋ + 1)-approximation algorithm for MVRST where Ds is the minimum diameter of spanning trees of G.
486376
Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts
For an edge weighted undirected graph G and an integer k ≥ 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts.We show that the performance ratio of our algorithm is 2 - 3/k for an odd k and 2 - (3k - 4)/(k2 - k) for an even k. The running time is O(kmn3 log(n2/m)) where n and m are the numbers of vertices and edges respectively.
13553903
Greedy splitting algorithms for approximating multiway partition problems
Abstract.Given a system (V,T,f,k), where V is a finite set, is a submodular function and k≥2 is an integer, the general multiway partition problem (MPP) asks to find a k-partition ={V1,V2,...,Vk} of V that satisfiesfor all i and minimizes f(V1)+f(V2)+···+f(Vk), where is a k-partition of hold. MPP formulation captures a generalization in submodular systems of many NP-hard problems such as k-way cut, multiterminal cut, target split and their generalizations in hypergraphs. This paper presents a simple and unified framework for developing and analyzing approximation algorithms for various MPPs.
18420967
A Primal-Dual Approximation Algorithm for the Survivable Network Design Problem in Hypergraph
Given a hypergraph with nonnegative costs on hyperedge and a requirement function r : 2V → Z+, where V is the vertex set, we consider the problem of finding a minimum cost hyperedge set F such that for all S ⊆ V, F contains at least r(S) hyperedges incident to S. In the case that r is weakly supermodular (i.e., r(V) = 0 and r(A) + r(B) ≤ max{r(A ∩ B) + r(A ∪ B); r(A - B) + r(B - A)} for any A;B ⊆ V), and the so-called minimum violated sets can be computed in polynomial time, we present a primal-dual approximation algorithm with performance guarantee dmaxH(rmax), where dmax is the maximum degree of the hyperedges with positive cost, rmax is the maximum requirement, and H(i) = Σi=1i 1/j is the harmonic function. In particular, our algorithm can be applied to the survivable network design problem in which the requirement is that there should be at least rst hyperedge-disjoint paths between each pair of distinct vertices s and t, for which rst is prescribed.
35924921
Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts
For an edge weighted undirected graph G and an integer k > 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts. We show that the performance ratio of our algorithm is 2 − 3/k for an odd k and 2 − (3k − 4)/(k2 − k) for an even k. The running time is O(kmn3 log(n2/m)) where n and m are the numbers of vertices and edges respectively.
14270828
A Strict Approach to Approximating Lognormal Sum Distributions
In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RV). The least squares curve fitting technique is first used to obtain the approximated closed-form pdf of the sum RV. The second time use of the least squares curve fitting technique brings the explicit closed-form expressions of the coefficients as a function of the number of the summands and the dB spread of the summands. Simulation results show that the proposed approximation exhibits a good match with the simulation results in the interested range of the distributions of the summands. Furthermore, errors due to a mixed use of the sum RV in the domain of the original variable and the domain of the logarithm are pointed out and the corrected results are presented
31753599
Adaptive Closed-Loop Power Control Using an MMSE Receiver in DS-CDMA Systems
A closed-loop power control algorithm, which includes both power control and power allocation functions for DS-CDMA systems, is proposed. The target power level is updated by an iterative algorithm for a minimum mean square error (MMSE) linear filter receiver. The received power is compared with the target to generate the current power control command (PCC). The transmitted power is adjusted by applying a variable stepsize generator that utilizes the PCC history and the estimated mobile speed. Simulation results are presented to show the improvement of the proposed adaptive power control over the conventional fixed stepsize power control.
2050065
A Comparison of Sample-Path-Based Simulation-Optimization and Stochastic Decomposition for Multi-Location Transshipment Problems
Because of its applicability, as well as its generality, research in the area of simulation-optimization continues to attract significant attention. These methods, most of which rely on the statistically motivated search techniques, are at their best when very little is known about the structure of the function (e.g., function evaluations are treated as "blackbox" function-calls). In some applications such as the one discussed in this paper, objective function values may be obtained through linear/network flow optimization models. In such cases, the objective function may be convex, and in such circumstances, very large instances can be solved using stochastic programming techniques. This paper presents a computational case for using such techniques, whenever applicable
1964724
Optimal construction of edge-disjoint paths in random regular graphs
Given a graph G = (V, E) and a set of κ pairs of vertices in V, we are interested in finding, for each pair (ai, bi), a path connecting ai to bi such that the set of κ paths so found is edge-disjoint. (For arbitrary graphs the problem is NP-complete, although it is in P if κ is fixed.)We present a polynomial time randomized algorithm for finding edge-disjoint paths in the random regular graph Gn,r, for sufficiently large r. (The graph is chosen first, then an adversary chooses the pairs of end-points.) We show that almost every Gn,r is such that all sets of κ = Ω(n/log n) pairs of vertices can be joined. This is within a constant factor of the optimum.
19000804
Receive Side Coalescing for Accelerating TCP/IP Processing
With rapid advancements in Ethernet technology, Ethernet speeds have increased by 10 fold, from 1 to 10Gbps, in a period of 2-3 years. This sudden increase in speeds has outpaced the rate at which processor and memory speeds have been increasing, raising concerns that TCP/IP processing will not scale to these levels. As a result, applications running on commercial servers will not be able to take advantage of the increased Ethernet bandwidth. This has led to a flurry of activity in the industry and academia focused on finding ways to scale up TCP/IP processing to 10Gbps and beyond. In this paper, we propose a novel technique called "Receive Side Coalescing" (RSC) that increases TCP/IP processing efficiencies significantly. RSC allows NICs to identify packets that belong to same TCP/IP flow and coalesce them into a single large packet. As a result, TCP/IP stack has to process fewer packets reducing per packet processing costs. NIC can do this coalescing of packets during interrupt moderation time hence packet latency is not affected. We have collected packet traces and analyzed those to find out how much coalescing is possible in different scenarios. Our analysis shows that about 50% reduction in number of packets is possible. We have prototyped RSC on Windows and Linux to understand the benefits, and the results show that 2-7% of savings in CPU utilization is possible at 1Gbps speeds. Projection models developed to estimate processing costs at 10Gbps show that RSC can save up to 20% of the CPU.