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.
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.
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).
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.
10454756
Hardware Support for Accelerating Data Movement in Server Platform
Data movement (memory copies) is a very common operation during network processing and application execution on servers. The performance of this operation is rather poor on today's microprocessors due to the following aspects: 1) Several long-latency memory accesses are involved because the source and/or the destination are typically in memory, 2) latency hiding techniques, such as out-of-order execution, hardware threading, and prefetching, are not very effective for bulk data movement, and 3) microprocessors move data at register (small) granularity. In this paper, we show this overhead of bulk data movement and propose the use of dedicated copy engines to minimize it. We present a detailed analysis of copy engine architectures along two dimensions: 1) on-die versus off-die and 2) synchronous versus asynchronous. These copy engine architectures are superior to traditional direct memory access (DMA) engines because they are tightly coupled to the core architecture and enable lower overhead communication and signaling. We describe the hardware support required to implement these copy engines and integrate them into server platforms. We perform a detailed case study to evaluate the performance of these copy engines. The evaluation is based on an execution-driven simulator, which was extended with detailed models of copy engines. Our simulation results show that copy engines are effective in reducing the bulk data movement overhead and, hence, hold significant promise for high-performance server platforms
3098509
The nature of novelty detection
Sentence level novelty detection aims at spotting sentences with novel information from an ordered sentence list. In the task, sentences appearing later in the list with no new meanings are eliminated. For the task of novelty detection, the contributions of this paper are three-fold. First, conceptually, this paper reveals the computational nature of the task currently overlooked by the Novelty community—Novelty as a combination of partial overlap (PO) and complete overlap (CO) relations between sentences. We define partial overlap between two sentences as a sharing of common facts, while complete overlap is when one sentence covers all of the meanings of the other sentence. Second, technically, a novel approach, the selected pool method is provided which follows naturally from the PO-CO computational structure. We provide formal error analysis for selected pool and methods based on this PO-CO framework. We address the question how accurate must the PO judgments be to outperform the baseline pool method. Third, experimentally, results were presented for all the three novelty datasets currently available. Results show that the selected pool is significantly better or no worse than the current methods, an indication that the term overlap criterion for the PO judgments could be adequately accurate.
32435431
Regularized Semi-supervised Classification on Manifold
Semi-supervised learning gets estimated marginal distribution PX with a large number of unlabeled examples and then constrains the conditional probability p(y | x) with a few labeled examples. In this paper, we focus on a regularization approach for semi-supervised classification. The label information graph is first defined to keep the pairwise label relationship and can be incorporated with neighborhood graph which reflects the intrinsic geometry structure of PX. Then we propose a novel regularized semi-supervised classification algorithm, in which the regularization term is based on the modified Graph Laplacian. By redefining the Graph Laplacian, we can adjust and optimize the decision boundary using the labeled examples. The new algorithm combines the benefits of both unsupervised and supervised learning and can use unlabeled and labeled examples effectively. Encouraging experimental results are presented on both synthetic and real world datasets.
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
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