arXiv subjects

Max Ilsen

Publications and source records attributed to Max Ilsen.

6 recordsLinked to original sources

arXiv2026

Designing Capacitated Subnetworks for Shortest Path Routing

In pursuit of higher energy efficiency in computer networks, one subfield of green traffic engineering aims at reducing the size of a network during times of low traffic, while still guaranteeing the ability to route all occurring demands. In this setting, we have to simultaneously solve a network design problem (choosing connections to deactivate) and a routing problem (routing paths in the active subnetwork, adhering to some routing protocol). Interestingly, there seems to be no available method to tackle the problem as a whole for the simplest (and still most commonly used) routing paradigm: shortest path routing. State-of-the-art methods either do not consider capacities, or assume that the routing paths should not change when deactivating network connections, or separate the problem into its two constituents, first solving the network design problem (using some estimators in lieu of the precise routing protocol) and only then the actual routing problem. In this paper, we present an algorithm to tackle the full combined problem exactly via a novel integer linear program, modeling dynamically changing shortest paths. To solve it, we need to devise a special-purpose column generation method. To speed up the solution process, we further propose additional provably strengthening constraints. Now having the means to yield true optimal solutions for (small) practical instances, we can for the first time give an in-depth experimental evaluation that includes the absolute quality intrinsic to the above simplifying algorithms. It turns out that the arguably simplest method--first computing a routing, fixing it, and turning off all superfluous connections--yields solutions surprisingly close to the true optimum in practice. When considering multiple different traffic demands, a recent traffic-oblivious approach (TOCA) performs best, while being comparatively straightforward to implement.

cs.DS↗

arXiv2026

No Traffic to Cry: Traffic-Oblivious Link Deactivation for Green Traffic Engineering

As internet traffic grows, the underlying infrastructure consumes increasing amounts of energy. During off-peak hours, large parts of the networks remain underutilized, presenting significant potential for energy savings. Existing Green Traffic Engineering approaches attempt to leverage this potential by switching off those parts of the networks that are not required for the routing of specific traffic matrices. When traffic changes, the approaches need to adapt rapidly, which is hard to achieve given the complexity of the problem. We take a fundamentally different approach: instead of considering a specific traffic matrix, we rely on a traffic-oblivious routing scheme. We discuss the NP-hard problem of activating as few connections as possible while still guaranteeing that any down-scaled traffic matrix $\varrho\cdot T$ can be routed, where $\varrho \in (0,1)$ and $T$ is any traffic matrix routable in the original network. We present a $\max(\frac{1}{\varrho\cdot\lambda_{\text{min}}},2)$-approximation algorithm for this problem, with $\lambda_{\text{min}}$ denoting the minimum number of connections between any two connected routers. Additionally, we propose two post-processing heuristics to further improve solution quality. Our evaluation shows that we can quickly generate near-optimal solutions. By design, our method avoids the need for frequent reconfigurations and offers a promising direction to achieve practical energy savings in backbone networks.

cs.NI↗

arXiv2025

Traffic-Oblivious Multi-Commodity Flow Network Design

We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph $G$ with edge capacities $\mathit{cap}$ and a retention ratio $\alpha\in(0,1)$, find an edge-wise minimum subgraph $G' \subseteq G$ such that for all traffic matrices $T$ routable in $G$ using a multi-commodity flow, $\alpha\cdot T$ is routable in $G'$. This natural yet novel problem is motivated by recent research that investigates how the power consumption in backbone computer networks can be reduced by turning off connections during times of low demand without compromising the quality of service. Since the actual traffic demands are generally not known beforehand, our approach must be traffic-oblivious, i.e., work for all possible sets of simultaneously routable traffic demands in the original network. In this paper we present the problem, relate it to other known problems in literature, and show several structural results, including a reformulation, maximum possible deviations from the optimum, and NP-hardness (as well as a certain inapproximability) already on very restricted instances. The most significant contribution is a $\max(\frac{1}{\alpha}, 2)$-approximation based on a surprisingly simple LP-rounding scheme. We also give instances where this worst-case approximation ratio is met and thus prove that our analysis is tight.

cs.DS↗

arXiv2023

Green Traffic Engineering by Line Card Minimization

Green Traffic Engineering encompasses network design and traffic routing strategies that aim at reducing the power consumption of a backbone network. We argue that turning off linecards is the most effective approach to reach this goal. Thus, we investigate the problem of minimizing the number of active line cards in a network while simultaneously allowing a multi-commodity flow being routed and keeping the maximum link utilization below a certain threshold. In addition to proving this problem to be NP-hard, we present an optimal ILP-based algorithm as well as a heuristic based on 2-Segment Routing. Lastly, we evaluate both approaches on real-world networks obtained from the Repetita Framework and a globally operating Internet Service Provider. The results of this evaluation indicate that our heuristic is not only close to optimal but significantly faster than the optimal algorithm, making it viable in practice.

cs.NI↗

arXiv2023

Directed Capacity-Preserving Subgraphs: Hardness and Exact Polynomial Algorithms

We introduce and discuss the Minimum Capacity-Preserving Subgraph (MCPS) problem: given a directed graph and a retention ratio $\alpha \in (0,1)$, find the smallest subgraph that, for each pair of vertices $(u,v)$, preserves at least a fraction $\alpha$ of a maximum $u$-$v$-flow's value. This problem originates from the practical setting of reducing the power consumption in a computer network: it models turning off as many links as possible while retaining the ability to transmit at least $\alpha$ times the traffic compared to the original network. First we prove that MCPS is NP-hard already on a restricted set of directed acyclic graphs (DAGs) with unit edge capacities. Our reduction also shows that a closely related problem (which only considers the arguably most complicated core of the problem in the objective function) is NP-hard to approximate within a sublogarithmic factor already on DAGs. In terms of positive results, we present two algorithms that solve MCPS optimally on directed series-parallel graphs (DSPs): a simple linear-time algorithm for the special case of unit edge capacities and a cubic-time dynamic programming algorithm for the general case of non-uniform edge capacities. Further, we introduce the family of laminar series-parallel graphs (LSPs), a generalization of DSPs that also includes cyclic and very dense graphs. Their properties allow us to solve MCPS on LSPs by employing our DSP-algorithms as subroutines. In addition, we give a separate quadratic-time algorithm for MCPS on LSPs with unit edge capacities that also yields straightforward quadratic time algorithms for several related problems such as Minimum Equivalent Digraph and Directed Hamiltonian Cycle on LSPs.

cs.DS↗

arXiv2021

Star-Struck by Fixed Embeddings: Modern Crossing Number Heuristics

We present a thorough experimental evaluation of several crossing minimization heuristics that are based on the construction and iterative improvement of a planarization, i.e., a planar representation of a graph with crossings replaced by dummy vertices. The evaluated heuristics include variations and combinations of the well-known planarization method, the recently implemented star reinsertion method, and a new approach proposed herein: the mixed insertion method. Our experiments reveal the importance of several implementation details such as the detection of non-simple crossings (i.e., crossings between adjacent edges or multiple crossings between the same two edges). The most notable finding, however, is that the insertion of stars in a fixed embedding setting is not only significantly faster than the insertion of edges in a variable embedding setting, but also leads to solutions of higher quality.

cs.DM↗