Computing shortest paths for any number of hops

Abstract

In this paper, we introduce and investigate a "new" path optimization problem that we denote the all hops optimal path (AHOP) problem. The problem involves identifying, for all hop counts, the optimal, i.e., minimum weight, path(s) between a given source and destination(s). The AHOP problem arises naturally in the context of quality-of-service (QoS) routing in networks, where routes (paths) need to be computed that provide services guarantees, e.g., delay or bandwidth, at the minimum possible "cost" (amount of resources required) to the network. Because service guarantees are typically provided through some form of resource allocation on the path (links) computed for a new request, the hop count, which captures the number of links over which resources are allocated, is a commonly used cost measure. As a result, a standard approach for determining the cheapest path available that meets a desired level of service guarantees is to compute a minimum hop shortest (optimal) path. Furthermore, for efficiency purposes, it is desirable to precompute such optimal minimum hop paths for all possible service requests. Providing this information gives rise to solving the AHOP problem. The paper's contributions are to investigate the computational complexity of solving the AHOP problem for two of the most prevalent cost functions (path weights) in networks, namely, additive and bottleneck weights. In particular, we establish that a solution based on the Bellman-Ford algorithm is optimal for additive weights, but show that this does not hold for bottleneck weights for which a lower complexity solution exists. KeywordsHop-restricted shortest paths, maximum bandwidth, minimum delay, networks, quality-of-service routing This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/28 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 10, NO. 5, OCTOBER 2002 613 Computing Shortest Paths for Any Number of Hops Roch Guérin, Fellow, IEEE, and Ariel Orda, Senior Member, IEEE Abstract-In this paper, we introduce and investigate a "new" path optimization problem that we denote the all hops optimal path (AHOP) problem. The problem involves identifying, for all hop counts, the optimal, i.e., minimum weight, path(s) between a given source and destination(s). The AHOP problem arises naturally in the context of quality-of-service (QoS) routing in networks, where routes (paths) need to be computed that provide services guarantees, e.g., ...

Optimal placement of UV-based communications relay nodes

“…We will consider here the AHOP problem [23]. It consists in finding a k-restricted cheapest path from a selected node s to all j ∈ N for each k = 1, 2, .…”

“…4, we address also the more general problem of finding optimal placement of a limited number of communications relay nodes for every possible discrete target position. It is reduced to the all hops optimal path (AHOP) problem [23]. The consideration of this more general problem allows us to move the major computational burden on the mentioned presolving stage.…”

Research challenges in QoS routing

“…Some of the proposed heuristics only target special cases of the MC(O)P problem. For instance, when bandwidth is one of the constraints that must be satisfied by the path computation algorithm, the MCP problem is defined as a Bandwidth Restricted Path (BRP) problem [6][7][8][9][10]. Another popular subproblem is called Restricted Shortest Path (RSP) problem [11][12][13].…”

“…Secondly, it requires the application of the path computation algorithm for each connection request, introducing additional processing overhead on the routers, especially when the arrival rate of connection requests is high. The pre-computation of paths is the alternative approach to handle the problem of the processing overhead associated with on-demand path computation at the expense of the eventual inaccuracy of the routing decision [7] and [29].…”

Inter-domain QoS routing on Diffserv networks: a region-based approach

“…Another important measure we considered when evaluating our architecture is whether our architecture imposes additional traffic on the Internet or not, which is also used as a measure for analysis by G. Apostolopoulos et al [17]. This measure is evaluated by the average number of hops in the shortest paths.…”