41378670
A Unified Framework for Approximating Multiway Partition Problems
We present a simple and unified framework for developing and analyzing approximation algorithms for some multiway partition problems (with or without terminals), including the k-way cut (or kcut), multiterminal cut (or multiway cut), hypergraph partition and target split.
44859876
A primal-dual approximation algorithm for the survivable network design problem in hypergraphs
Given a hypergraph with nonnegative costs on hyperedges, and a weakly supermodular function r:2V → Z+, where V is the vertex set, we consider the problem of finding a minimum cost subset of hyperedges such that for every set S ⊆ V, there are at least r(S) hyperedges that have at least one but no all endpoints in S. This problem captures a hypergraph generalization of the survivable network design problem (SNDP), and also the element connectivity problem (ECP). We present a primal-dual algorithm with a performance guarantee of dmax+H (rmax), where dmax+ is the maximum degree of hyperedges of positive costs, rmax = maxs r(S), and H(k) = 1 + 1/2 +...+ 1/k. In particular, our result contains a 2H(rmax)-approximation algorithm for ECP, which gives an independent and complete proof for the result first obtained by Jain et al. (Proceedings of the SODA, 1999, p. 484-489).
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.
8864219
On generalized greedy splitting algorithms for multiway partition problems
Given a system (V,T,f,k) where V is a finite set, T ⊆ V, f : 2V → R is a submodular function and k ≥ 2 is an integer, the multiway partition problem (MPP) asks to find a k-partition P = {V1, V2,...,Vk} of V that satisfies Vi ∩ T ≠ 0 for all i and minimizes f(V1) + f(V2)+...+f(Vk). This formulation captures a generalization of many NP-hard partition problems in graphs or hypergraphs. Previously, the authors have shown a simple framework for approximating MPPs by greedily increasing the size of partition by one. In this paper, we show that, if T = V, improved guarantees are available by greedily increasing the size by two. We also show polynomial time implementations for several problem classes.
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.
6425229
A linear time 5/3-approximation for the minimum strongly-connected spanning subgraph problem
A linear time 5/3-approximation algorithm is presented for the NP-hard problem of finding a minimum strongly-connected spanning subgraph. It is based on cycle contraction that was first introduced by Khuller, Raghavachari and Young [SIAM J. Comput. 24 (1995) 859-872]. We improve their result by contracting special cycles and utilizing a more efficient data structure.
5957902
Qualitative and quantitative car tracking from a range image sequence
In this paper, we present a car tracking system which provides quantitative and qualitative motion estimates of the tracked car simultaneously from a moving observer. First, we construct three motion models (constant velocity, constant acceleration, and turning) to describe the qualitative motion of a moving car. Then the models are incorporated into the Extended Kalman Filters to perform quantitative tracking. Finally, we develop, an Extended Interacting Multiple Model (EIMM) algorithm to manage the switching between models and to output both qualitative and quantitative motion estimates of the tracked car. Accurate motion modeling and efficient model management result in a high performance tracking system. The experimental results on simulated and real data demonstrate that our tracking system is reliable and robust, and runs in real-time. The multiple motion representations make the system useful in various autonomous driving tasks.
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
13014348
QoS policies and architecture for cache/memory in CMP platforms
As we enter the era of CMP platforms with multiple threads/cores on the die, the diversity of the simultaneous workloads running on them is expected to increase. The rapid deployment of virtualization as a means to consolidate workloads on to a single platform is a prime example of this trend. In such scenarios, the quality of service (QoS) that each individual workload gets from the platform can widely vary depending on the behavior of the simultaneously running workloads. While the number of cores assigned to each workload can be controlled, there is no hardware or software support in today's platforms to control allocation of platform resources such as cache space and memory bandwidth to individual workloads. In this paper, we propose a QoS-enabled memory architecture for CMP platforms that addresses this problem. The QoS-enabled memory architecture enables more cache resources (i.e. space) and memory resources (i.e. bandwidth) for high priority applications based on guidance from the operating environment. The architecture also allows dynamic resource reassignment during run-time to further optimize the performance of the high priority application with minimal degradation to low priority. To achieve these goals, we will describe the hardware/software support required in the platform as well as the operating environment (O/S and virtual machine monitor). Our evaluation framework consists of detailed platform simulation models and a QoS-enabled version of Linux. Based on evaluation experiments, we show the effectiveness of a QoS-enabled architecture and summarize key findings/trade-offs.
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
38902380
Construction Algorithm of Principal Curves in the Sense of Limit
Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.