arXiv subjects

Edgar Perner

Publications and source records attributed to Edgar Perner.

2 recordsLinked to original sources

arXiv2026

Pairwise Reconnection for Cost-Distance Steiner Trees

The Uniform Cost-Distance Steiner Tree Problem asks for a rooted tree that minimizes the connection cost plus a weighted sum of root-to-terminal distances. We develop an algorithm that constructs two candidate trees: one based on direct connections to the root and another that pairs selected vertices and connects each pair to the root. The algorithm selects the tree with the smaller objective value. The resulting randomized algorithm achieves expected approximation factors of $1.698$ in the spanning case and $2.041$ in the general case, and it can be derandomized in polynomial time. The pairwise matching analysis charges part of the augmentation cost directly to the connection and delay costs of an optimal solution, rather than only to the separated lower bound used in previous analyses. This allows the $1.698$ factor to fall below the maximum multiplicative gap of $1+1/\sqrt{2}$ between the optimum value and that lower bound. We give instance families with approximation-ratio lower bounds approaching $1+1/\sqrt{2}$ for cut-and-reconnect algorithms that start from a minimum spanning tree and $3/2$ for the present algorithm. Finally, we show that the Uniform Cost-Distance Steiner Tree Problem and the Steiner-tree version of the Cable-Trench Problem are approximation equivalent up to an arbitrarily small additive loss.

cs.DS↗

arXiv2025

Cost-Distance Steiner Trees for Timing-Constrained Global Routing

The cost-distance Steiner tree problem seeks a Steiner tree that minimizes the total congestion cost plus the weighted sum of source-sink delays. This problem arises as a subroutine in timing-constrained global routing with a linear delay model, used before buffer insertion. Here, the congestion cost and the delay of an edge are essentially uncorrelated, unlike in most other algorithms for timing-driven Steiner trees. We present a fast algorithm for the cost-distance Steiner tree problem. Its running time is $\mathcal{O}(t(n \log n + m))$, where $t$, $n$, and $m$ are the numbers of terminals, vertices, and edges in the global routing graph. We also prove that our algorithm guarantees an approximation factor of $\mathcal{O}(\log t)$. This matches the best-known approximation factor for this problem, but with a much faster running time. To account for increased capacitance and delays after buffering caused by bifurcations, we incorporate a delay penalty for each bifurcation without compromising the running time or approximation factor. In our experimental results, we show that our algorithm outperforms previous methods that first compute a Steiner topology, e.g. based on shallow-light Steiner trees or the Prim-Dijkstra algorithm, and then embed this into the global routing graph.

cs.DS↗