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.
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.
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.
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.
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.
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.
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.
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.
15509008
Exploring Small-Scale and Large-Scale CMP Architectures for Commercial Java Servers
As we enter the era of chip multiprocessor (CMP) architectures, it is important that we explore the scaling characteristics of mainstream server workloads on these platforms. In this paper, we analyze the performance of an Enterprise Java workload (SPECjbb2005) on two important classes of CMP architectures. One class of CMP platforms comprise of "small-scale" CMP (SCMP) processors with a few large out-of order cores on the die. Another class of CMP platforms comprise of "large-scale" CMP (LCMP) processors) with several small in-order cores on the die. For these classes of CMP architectures to succeed, it is important that there are sufficient resources (cache, memory and interconnect) to allow for a balanced scalable platform. In this paper, we focus on evaluating the resource scaling characteristics (cores, caches and memory) of SPECjbb2005 on these two architectures and understanding architectural trade-offs that may be required in future CMP offerings. The overall evaluation is uniquely conducted using four different methodologies (measurements on latest platforms, trace-based cache simulation, trace-based platform simulation and execution-driven emulation). Based on our findings, we summarize the architectural recommendations for future CMP server platforms (e.g. the need for large DRAM caches)