20672183
An Algorithm to Construct k-Regular k-Connected Graphs with the Maximum k-Diameter
Abstract. Let f(2m,k) be the Maximum k-diameter of k-regular k-connected graphs on 2m vertices. In this paper we give an algorithm and prove that we can construct k-regular k-connected graphs on 2m vertices with the maximum k-diameter using it. We also prove some known results about f(2m,k) and verify that we can get some unknown values of f(2m,k) by our algorithm.
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.
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
14245590
RED with optimized dynamic threshold deployment on shared buffer
Prior survey of RED algorithm deployment on multiqueue system with shared buffer was unfair and sensitive to congestion level by statically setting the parameters. In this paper, our goal is to deploy the Random Early Detection (RED) algorithm in routers on shared buffer and solve these problems. A novel buffer management scheme that dynamically adjusts the parameters of RED named RED-ODT is proposed. Simulations under uniform traffic load and nonuniform traffic load are given, the results of which ascertain and demonstrate the superiority of the proposed scheme in terms of low packet drop ratio, satisfying buffer utilization and fairness. Simulation also shows that RED-ODT is insensitive to congestion level.
5800626
Hybrid Cache Architecture for High Speed Packet Processing
The exposed memory hierarchies employed in many network processors (NPs) are expensive and hard to be effectively utilized. On the other hand, conventional cache cannot be directly incorporated into NP either because of its low efficiency in locality exploitation for network applications. In this paper, a novel memory hierarchy component, called split control cache, is presented. The proposed scheme employs two independent low latency memory stores to temporarily hold the flow-based and application-relevant information, exploiting the different locality behaviors exhibited by these two types of data. Data movement is manipulated by specially designed hardware to relieve the programmers from details of memory management. Performance evaluation shows that this component can achieve a hit rate of over 90% with only 16 KB of memories in route lookup under link rate of OC-3c and provide enough flexibility for the implementation of most network applications.
800712
On the autocorrelation structure of TCP traffic
The statistical characteristics of network traffic--in particular the observation that it can exhibit long range dependence--have received considerable attention from the research community over the past few years. In addition, the recent claims that the TCP protocol can generate traffic with long range dependent behavior has also received much attention. Contrary to the latter claims, in this paper we show that the TCP protocol can generate traffic with correlation structures that spans only an analytically predictable finite range of time-scales. We identify and analyze separately the two mechanisms within TCP that are responsible for this scaling behavior: timeouts and congestion avoidance. We provide analytical models for both mechanisms that, under the proper loss probabilities, accurately predict the range in time-scales and the strength of the sustained correlation structure of the traffic sending rate of a single TCP source. We also analyze an existing comprehensive model of TCP that accounts for both mechanisms and show that TCP itself exhibits a predictable finite range of time-scales under which traffic presents sustained correlations. Our claims and results are derived from Markovian models that are supported by simulations. We note that traffic generated by TCP can be misinterpreted to have long range dependence, but that long range dependence is not possible due to inherent finite time-scales of the mechanisms of TCP.
21236644
Parallel Switch System with QoS Guarantee for Real-Time Traffic
This paper studies the load-balancing algorithm and quality of service (QoS) control mechanism in a 320Gb/s switch system, which incorporates four packet-level parallel switch planes. Eight priorities for both unicast and multicast traffic are implemented, and the highest priority with strict QoS guarantee is designed for real-time traffic. Through performance analysis under multi-priority burst traffic, we demonstrate that the load-balancing algorithm is efficient, and the switch system not only provides excellent performance to real-time traffic, but also efficiently allocates bandwidth among other traffic of lower priorities. As a result, this parallel switch system is more scalable towards next generation core routers with QoS guarantee, as well as ensures in-order delivery of IP packets.
1437746
On the skew-bounded minimum-buffer routing tree problem
Bounding the load capacitance at gate outputs is a standard element in today's electrical correctness methodologies for high-speed digital very large scale integration design. Bounds on load caps improve coupling-noise immunity, reduce degradation of signal transition edges, and reduce delay uncertainty due to coupling noise (Kahng et al. 1998). For clock and test distribution, an additional design requirement is bounding the buffer skew, i.e., the difference between the maximum and the minimum number of buffers over all of the source-to-sink paths in the routing tree, since buffer skew is one of the main factors affecting delay skew (Tellez and Sarrafzadeh 1997). In this paper, we consider algorithms for buffering a given tree with the minimum number of buffers under given load cap and buffer skew constraints. We show that the greedy algorithm proposed by Tellez and Sarrafzadeh is suboptimal for nonzero buffer-skew bounds and give examples showing that no bottom-up greedy algorithm can achieve optimality. The main contribution of the paper is an optimal dynamic programming algorithm for the problem. Experiments on test cases extracted from recent industrial designs show that the dynamic programming algorithm has practical running time and saves up to 37.5% of the buffers inserted by Tellez and Sarrafzadeh's algorithm.