On Hamiltonian cycles and Hamiltonian paths

Rahman, M. Sohel; Kaykobad, M.

doi:10.1016/j.ipl.2004.12.002

Cited by 59 publications

(34 citation statements)

References 7 publications

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“…Rahman and Kaykobad [3] proved the following theorem on Hamiltonian paths in graphs. At the end of [3] Rahman and Kaykobad asked if one can find a condition which is similar as the one in Theorem 1 for Hamiltonian cycles in graphs.…”

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confidence: 99%

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A new sufficient condition for Hamiltonicity of graphs

2006

Information Processing Letters

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confidence: 99%

“…At the end of [3] Rahman and Kaykobad asked if one can find a condition which is similar as the one in Theorem 1 for Hamiltonian cycles in graphs. The main result in this note is the following Theorem 2.…”

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confidence: 99%

A new sufficient condition for Hamiltonicity of graphs

2006

Information Processing Letters

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“…Rahaman and Kaykobad presented [38] a sufficient condition for the existence of Hamilton Path in a graph basing upon a shortest distance so the parameter , u v which denotes the length of the shortest path between u and v . In homogenous WSN, clusters always form in the homogeny structure.…”

Section: Definition Of Hamilton Path and Hamilton Circuitmentioning

confidence: 99%

HEER – A delay-aware and energy-efficient routing protocol for wireless sensor networks

Yang

2016

Computer Networks

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Abstract-Minimizing energy consumption to maximize network lifetime is one of the crucial concerns in designing wireless sensor network routing protocols. Cluster-based protocols have shown promising energy-efficiency performance, where sensor nodes take turns to act as cluster heads (CHs), which carry out higher-level data routing and relaying. In such case the energy consumption is more evenly distributed for all the nodes. However, most cluster-based protocols improve energy-efficiency at the cost of transmission delay. In this paper, we propose an improved delay-aware and energy-efficient clustered protocol called Hamilton Energy-Efficient Routing Protocol (HEER). HEER forms clusters in the network initialization phase and links members in each cluster on a Hamilton Path, constructed using a greedy algorithm, for data transmission purpose. No cluster reformation is required and the members on the path will take turns to become cluster head. The design allows HEER to save on network administration energy and also balance the load comparing to traditional cluster-based protocols. The algorithms designed in HEER also means that it does not suffer long delay and does not require each node to have global location information comparing with classic chain-based protocols such as PEGASIS and its variations. We implemented the HEER protocol in MATLAB simulation and compared it with several cluster-based and chain-based protocols. We found that HEER is able to achieve an improved network lifetime over the current protocols while maintaining the average data transmission delay. In the simulation, HEER achieved 66.5% and 40.6% more rounds than LEACH and LEACH-EE, which are cluster-based protocols. When compared with chain-based protocols (PEGASIS and Intra-grid-PEGSIS), HEER managed 21.2 times and 16.7 times more rounds than PEGASIS and Intra-grid-PEGASIS respectively. In addition, HEER can eliminated 90% of transmission delay comparing to LEACH and LEACH-EE and 99% comparing with PEGASIS and Intra-grid-PEGASIS. Wireless communication is one of the major power consuming activities on SNs and its usage is controlled mainly by the routing protocol in action. An appropriate protocol design is therefore crucial for minimizing the energy consumption. There are three main types of routing protocols in WSNs, namely flat, hierarchical and location based protocols. KeywordsIn Flat routing protocol, all nodes communicate in a peer-to-peer manner without any hierarchy in the structure. The advantage is having a simple, expandable and low maintenance structure. However, it lacks local and central management of communication resource and usually suffers from long and varied delay.Location-based routing protocols, on the other hand, take in consideration of the location of SNs. Relative coordinates of neighbouring nodes can be extracted from the RF communication between them or, in some cases, by incorporating on-board GPS [3]. However, location tracking devices are huge energy consumers and their performance drops in harsh environme...

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“…But if a sufficient condition can be derived for a graph with diameter more than two, Hamiltonian path or cycle may be found with fewer edges. With this motivation, Rahman and Kaykobad [5] proposed a sufficient condition to find a Hamiltonian Path in a graph involving the parameter ( , V), which denotes the length of the shortest path between and V. Theorem 3 (see [5]). Let = ( , ) be a connected graph with vertices such that for all pairs of distinct nonadjacent vertices , V ∈ one has + V + ( , V) ≥ + 1.…”

Section: Then Has a Hamiltonian Cyclementioning

confidence: 99%