Ireneusz Olszewski | Searcharxiv

arXiv2026

Generic Dijkstra

The recently-proposed generic Dijkstra algorithm finds shortest paths in networks with continuous and contiguous resources. While the algorithm was proposed in the context of optical networks (and is applicable to other networks with finite and discrete resources), we present the stated problem in a broader algorithmic setting of the greedy approach. The algorithm was published without a proof of correctness, and with a minor shortcoming. We provide that missing proof and offer a correction to the shortcoming. To prove the algorithm correct, we generalize the greedy approach and the Bellman principle of optimality to algebraic structures with a partial ordering. By analyzing the size of the search space in the worst-case, we argue the stated problem is tractable. Thus we definitely answer a long-standing fundamental question of whether we can efficiently find a shortest path in a network with discrete resources subject to the continuity and contiguity constraints: yes, we can.

cs.NI↗

arXiv2024

Is dynamic dedicated path protection tractable?

Intractable is the problem of finding two link-disjoint paths of minimal cost if the path cost is limited since it can be a special case of the partition problem. In optical networks, this limit can be introduced by the signal modulation reach. Even without this limit, the existing literature suggested the problem intractable because of the spectrum continuity and contiguity constraints, but we show that the problem can be solved exactly with the recently-proposed generic Dijkstra algorithm over a polynomially-bounded search space, thus proving the problem tractable.

cs.NI↗

arXiv2021

Towards an efficient and exact algorithm for dynamic dedicated path protection

We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be applicable to other networks, where services have to be protected, and where the network resources are finite and discrete, e.g., wireless radio or networks capable of advance resource reservation. To the best of our knowledge, we are the first to propose an algorithm for this long-standing fundamental problem, which can be efficient and exact, as suggested by simulation results. The algorithm can be efficient because it can solve large problems, and it can be exact because its results are optimal, as demonstrated and corroborated by simulations. We offer a worst-case analysis to argue that the search space is polynomially upper bounded. Network operations, management, and control require efficient and exact algorithms, especially now, when greater emphasis is placed on network performance, reliability, softwarization, agility, and return on investment. The proposed algorithm uses our generic Dijkstra algorithm on a search graph generated "on-the-fly" based on the input graph. We corroborated the optimality of the results of the proposed algorithm with brute-force enumeration for networks up to 15 nodes large. We present the extensive simulation results of dedicated-path protection with signal modulation constraints for elastic optical networks of 25, 50, and 100 nodes, and with 160, 320, and 640 spectrum units. We also compare the bandwidth blocking probability with the commonly-used edge-exclusion algorithm. We had 48,600~simulation runs with about 41 million searches.

cs.NI↗