36855127
Some inequalities about connected domination number
Abstract Let G = ( V , E ) be a graph. In this note, γ c , ir, γ, i, β 0 , Γ, IR denote the connected domination number, the irredundance number, the domination number, the independent domination number, the independence number, the upper domination number and the upper irredundance number, respectively. We prove that γ c ⩽ 3 ir − 2 for a connected graph G . Thus, an open problem in Hedetniemi and Laskar (1984) discuss further some relations between γ c and γ, β 0 , Γ, IR, respectively.
31833569
The kth Lower Multiexponent of Tournament Matrices
10079260
The sum number and integral sum number of complete bipartite graphs
Let N denote the set of positive integers. The sum graph G + (S) of a 1nite subset S of N is the graph (S; E) with vertex set S and edge set E such that for u; v ∈ S; uv ∈ E if and only if u + v ∈ S. A graph G is called a sum graph if it is isomorphic to the sum graph G + (S) of some 1nite subset S of N . The sum number � (G) of a graph G is de1ned as the smallest nonnegative integer m for which G ∪ mK1 is a sum graph. Let Z be the set of all integers. By extending the set N to Z in the above de1nitions of sum graphs and sum numbers, Harary [3] introduced the corresponding notions of integral sum graphs and integral sum number of a graph. In this paper, we evaluate the value of the sum number and integral sum number of the complete bipartite graph Kr; s. While the former one corrects the result given in [4], the latter settles completely a problem proposed in [3]. c � 2001 Elsevier Science B.V. All rights reserved.
8364982
Supporting Complex Multi-Dimensional Queries in P2P Systems
More and more applications require peer-to-peer (P2P) systems to support complex queries over multi-dimensional data. For example, a P2P auction network for real estate frequently needs to answer queries such as "select five available buildings closest to the airport". Such queries are not efficiently supported in current P2P systems. Towards an efficient and scalable P2P system capable of processing complex multi-dimensional queries, the authors first proposed a comprehensive framework for sharing, indexing, and querying multi-dimensional data, where (i) peers with more computational power coordinate indexing and query processing, and (ii) other peers participate in part of the computation in order to achieve scalability and load-balance. Based on this framework, Network-R-tree (NR-tree), a P2P adaptation of the dominant spatial index - R*-tree was proposed. NR-tree, indexing spatial data at clustered peers, is capable of processing complex queries such as range queries and k-nearest neighbor queries. The authors proposed query processing algorithms for range and k-nearest neighbor queries and experimentally prove the effectiveness of proposed techniques with real data
5760901
Statistical gate delay calculation with crosstalk alignment consideration
We study gate delay variation caused by crosstalk aggressor alignment, i.e., difference of signal arrival times in coupled neighboring interconnects. This effect is as significant as multiple-input switching on gate delay variation [2]. We establish a functional relationship between driver gate delay and crosstalk alignment by deterministic circuit simulation, and derive closed form formulas for statistical distributions of driver gate delay and output signal arrival time.Our proposed method can be smoothly integrated into a static timing analyzer, which runtime is dominated by sampling deterministic delay calculation, while probabilistic computation and updating take constant time. Our experimental results on 70nm technology global interconnect structures and 130nm technology industry designs show respectively 159:4% and 147:4% differences in mean and standard deviation of gate delay without crosstalk aggressor alignment consideration, while our method gives within 2:57% and 3:86% offset in gate output signal arrival time mean and standard deviation, respectively.
3063801
Iteration-Shared Scheduling Algorithms Abolishing the Departure-Time-Compatible Graph in Switch-Memory-Switch Switches
Switch-Memory-Switch (SMS) architecture exhibits an excellent performance due to its emulating the Output Queueing structure. However, in order to achieve the maximal matching, the first stage scheduling operates at a huge computational complexity, which blocks the SMS from practical implementation. In order to put SMS into more effective industrial applications, especially in super-large size switches/routers with multi-services environment, two parallel iterative scheduling algorithms, named IS-RRM and AIS-RRM respectively, are proposed in this paper. The algorithms abolish totally the traditional departure-time-compatible (DTC) graph, and by using iteration-sharing technology, greatly reduce the required iteration number in each time slot. Using a discrete-time Markov chain to model the AIS-RRM algorithm, we obtain its upper bound of cell loss rate. Meanwhile, experimental and theoretical results show that so long as the number of shared memories is twice the switch size, AIS-RRM algorithm can achieve a cell loss rate of 10 when the input buffer size is 15 and the iteration number of each time slot is 6, despite the arrival traffic pattern and the switch size. Furthermore, the iteration number required in each time slot can be further decreased by increasing the input buffer size.
2853015
On the capacity of hybrid wireless networks
This paper involves the study of the throughput capacity of hybrid wireless networks. A hybrid network is formed by placing a sparse network of base stations in an ad hoc network. These base stations are assumed to be connected by a high-bandwidth wired network and act as relays for wireless nodes. They are not data sources nor data receivers. Hybrid networks present a tradeoff between traditional cellular networks and pure ad hoc networks in that data may be forwarded in a multihop fashion or through the infrastructure. It has been shown that the capacity of a random ad hoc network does not scale well with the number of nodes in the system. In this work, we consider two different routing strategies and study the scaling behavior of the throughput capacity of a hybrid network. Analytical expressions of the throughput capacity are obtained. For a hybrid network of n nodes and m base stations, the results show that if m grows asymptotically slower than √n, the benefit of adding base stations on capacity is insignificant. However, if m grows faster than √n, the throughput capacity increases linearly with the number of base stations, providing an effective improvement over a pure ad hoc network. Therefore, in order to achieve nonnegligible capacity gain, the investment in the wired infrastructure should be high enough.
53249400
Non-tree routing for reliability and yield improvement
We propose to introduce redundant interconnects for manufacturing yield and reliability improvement. By introducing redundant interconnects, the potential for open faults is reduced at the cost of increased potential for short faults; overall, manufacturing yield and fault tolerance can be improved. We focus on a post-processing, tree augmentation approach which can be easily integrated in current physical design flows. Experiments on randomly generated and industry testcases show that our greedy augmentation method achieves significant increase in reliability (as measured by the percentage of biconnected tree edges) with very small increase in wirelength. SPICE simulations imply that non-tree routing has smaller delay variation due to process variability.