Finding multi-constrained feasible paths by using depth-first search
An extended depth-first-search (EDFS) algorithm is proposed to solve the multi-constrained path (MCP) problem in quality-of-service (QoS) routing, which is NP-Complete when the number of independent routing constraints is more than one. EDFS solves the general k-constrained MCP problem with pseudo-polynomial time complexity O(m^2 * EN + N^2), where m is the maximum number of non-dominated paths maintained for each destination, E and N are the number of links and nodes of a graph, respectively. This is achieved by deducing potential feasible paths from knowledge of previous explorations, without re-exploring finished nodes and their descendants in the process of the DFS search. One unique property of EDFS is that the tighter the constraints are, the better the performance it can achieve, w.r.t. both time complexity and routing success ratio. This is valuable to highly dynamic environment such as wireless ad hoc networks in which network topology and link state keep changing, and real-time or multimedia applications that have stringent service requirements. EDFS is an independent feasible path searching algorithm and decoupled from the underlying routing protocol, and as such can work together with either proactive or on-demand ad hoc routing protocols as long as they can provide sufficient network state information to each source node. Analysis and extensive simulation are conducted to study the performance of EDFS in finding feasible paths that satisfy multiple QoS constraints. The main results show that EDFS is insensitive to the number of constraints, and outperforms other popular MCP algorithms when the routing constraints are tight or moderate. The performance of EDFS is comparable with that of the other algorithms when the constraints are loose.
Li, Z.; Garcia-Luna-Aceves, J. J. Finding multi-constrained feasible paths by using depth-first search. Wireless Networks. 2007 June; 13 (3): 323-334.