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.
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.
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.
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.
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
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.
31340161
The Empirical Impact of the Nature of Novelty Detection
Novelty detection systems aim at reducing redundant documents or sentences from a list of documents chronologically ordered. In the task, sentences appearing later in the list with no new meanings are eliminated. In an accompanying paper, the nature of novelty detection was revealed – Novelty as a combination of the PO (partial overlap) and CO (complete overlap) relations, which can be treated as two classification tasks; theoretical impacts were given. This paper provides what the nature of the task mean empirically. One new method – selected pool – implementing the nature of the task gained improvements on TREC Novelty datasets. New evaluation criteria are given, which are natural from the viewpoint of the nature of novelty detection.
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