Node-Constrained Traffic Engineering: Theory and Applications

Abstract

Traffic engineering (TE) is a fundamental task in networking. Conventionally, traffic can take any path connecting the source and destination. Emerging technologies such as segment routing, however, use logical paths going through a predetermined set of middlepoints. Inspired by this, in this work we introduce the problem of node-constrained TE, where traffic must go through a set of middlepoints, and study its theoretical fundamentals. We show that the general node-constrained TE that constrains the traffic to take paths going through one or more middlepoints is NP-hard for directed graphs but strongly polynomial for undirected graphs, unveiling a profound dichotomy between the two cases. We additionally investigate the popular variant of node-constrained TE that uses shortest paths between middlepoints, and show that the problem can now be solved in weakly polynomial time for a fixed number of middlepoints. Yet if we constrain the end-to-end paths to be acyclic, the problem can become NP-hard. This explains why existing work focuses on the computationally tractable variant. An important application of our work concerns the computational complexity of flow centrality, first proposed in 1991 by Freeman et al. [21]: we show that it is NP-hard for directed but strongly polynomial for undirected graphs. Finally, we investigate the middlepoint selection problem in general node-constrained TE. We introduce group flow centrality as a solution concept for multi-commodity networks, study its complexity, and show that it is monotone but not submodular for both directed and undirected graphs. Our work provides a thorough theoretical treatment of nodeconstrained TE and its applications.

Q-SR: An Extensible Optimization Framework for Segment Routing

“…Intra-segment routing: The intra-segment routing should be fully investigated, including link weights setting and intrasegment routing policy [7]. For instance, the intra-segment routing module can be replaced with other link-state routing policies or even a centralized min-cost MCF routing module.…”

“…All the 5 parallel paths, e.g. (1,2,6,7,11,12,16,17,21), from node 1 to 21 are fully utilized. On the other hand, the optimum can only be achieved when N r = N , more exactly N r = N − {1, 21}.…”

Traffic Engineering with Segment Routing under Uncertain Failures

“…The source node selects paths and guides the data packet to transmit along the paths in the network by inserting a sequenced segment list in the header of the data packet [9]. On the forwarding path, the network device that receives the data packet performs processing and forwarding operations according to this segment list [15]. Other nodes except the source node do not need to store and maintain any state information of the flow, so compared to the SDN architecture, SR saves the storage hardware of the forwarding table (such as ternary content addressable memory, TCAM) and thus has better scalability [22].…”

Segment Routing: a Comprehensive Survey of Research Activities, Standardization Efforts and Implementation Results

“…In [110], the node constrained TE problem is defined and analyzed, and SR is claimed to be an enabling technology for such routing strategies. This problem consists in the optimization of one of these two objectives: maximize the network throughput, or minimize the maximum congestion.…”