routing

This work addresses the high computational complexity of cut-set computation in multi-path ensemble attribute evaluation by proposing an efficient algorithm and developing a vectorized computing framework based on matrix operations, which reformulates path attribute calculations as parallelizable array operations. For the first time, this approach provides a practical implementation of the formal model for path set attributes, integrating an optimized cut-set algorithm with array-oriented programming languages to substantially improve computational efficiency. Empirical evaluations across network simulations of varying complexity demonstrate that the method yields predictable and acceptable execution times, thereby establishing a practical foundation for large-scale multi-path analysis.

Existing approaches in network systems and graph theory lack formal models and scoring mechanisms for *sets of paths*—focusing instead on individual paths, thereby failing to capture inter-path attribute dependencies and contextual interactions in complex networks. Method: This paper proposes the first functional attribute modeling framework specifically designed for path sets. Departing from conventional single-path evaluation paradigms, it employs graph-theoretic formalization and functional modeling to rigorously characterize attribute dependencies among multiple paths, and constructs an extensible feature representation system for path sets. It further introduces an attribute context analysis mechanism to enable fine-grained, scenario-aware evaluation of path combinations under diverse network conditions. Contribution/Results: The resulting general-purpose path set attribute computation model significantly improves the accuracy and environmental adaptability of path selection. It provides both theoretical foundations and practical tools for multi-path decision-making in dynamic and heterogeneous network environments.

This study addresses energy efficiency optimization in communication networks during low-traffic periods by jointly optimizing network topology design and shortest-path routing. The approach ensures that all traffic demands can be satisfied within the activated subnetwork through dynamically adapted shortest paths. The authors propose, for the first time, a capacitated integer linear programming model that precisely captures dynamic shortest-path routing, complemented by provably effective strengthening constraints to accelerate solution convergence. A tailored column generation algorithm is developed to efficiently handle large-scale instances. Experimental results demonstrate that a simplified strategy—fixing routes and deactivating redundant links—achieves near-optimal performance, while the traffic-oblivious method TOCA exhibits superior efficacy in multi-demand scenarios.

Real-world infrastructure networks often exhibit structural incompleteness and require multidimensional evaluation criteria, yet traditional pathfinding methods are limited by their reliance on complete graph structures and scalar optimization objectives. This work proposes the concept of “traversal,” which unifies existing edges with constructible gap connections into a single modeling framework, treating plannable connections as first-class transformation units for the first time. The approach supports non-scalar trade-offs, conditional feasibility checks, and policy calibration. By integrating a parameterized traversal framework, an efficient candidate filtering mechanism, and multidimensional termination criteria, the method bridges graph-based reasoning with engineering feasibility assessment. Empirical validation on data center circuit design and optical communication routing tasks demonstrates its effectiveness, significantly enhancing both expressiveness and practical utility.

This work addresses the open problem of efficiently maintaining a low-stretch, small-size, and rapidly updatable graph spanner in fully dynamic graphs under an adaptive adversary. The paper presents the first deterministic fully dynamic algorithm for this setting, whose core innovation is the introduction of a “low-diameter router decomposition”—a genuine decomposition technique that partitions the graph into edge-disjoint clusters with limited vertex overlap, ensuring internally closed paths within each cluster and enabling low-congestion multi-commodity flow routing. This approach achieves, for the first time, polynomial stretch, near-linear size ($O(n^{1+O(1/k)})$), and sublinear worst-case update time ($n^{O(\delta)}$) for any $512 \leq k \leq (\log n)^{1/49}$ and $1/k \leq \delta \leq 1/400$. The framework further extends to fault-tolerant and low-congestion spanner constructions.

This work addresses the challenge of efficiently maintaining breadth-first search (BFS) structures under dynamic edge insertions and deletions in directed graphs. It presents the first fully dynamic BFS framework that simultaneously preserves the BFS spanning tree, node levels, and BFS ordering. By integrating novel dynamic data structures with incremental update strategies, the approach cohesively handles the impact of edge modifications on single-source shortest paths and reachability. This study bridges a critical gap in the theoretical understanding of fully dynamic BFS for directed graphs and provides both foundational insights and practical tools for dynamic graph algorithms.

This work addresses the problem of efficient routing between arbitrary pairs of vertices in a planar domain containing multiple disjoint convex polygonal obstacles. The authors propose a recursive routing scheme that relies solely on local information, achieved through geometric recursive partitioning, compact label encoding, and the construction of localized routing tables. The scheme guarantees a path stretch factor of $(7+\varepsilon)\log h$, where $h$ is the number of obstacles, while using vertex labels of size $O(\sqrt{h}\log h\log n)$. The routing table size nearly matches the known theoretical lower bound, and the preprocessing time is $O(n^2\log n)$. This approach strikes a favorable balance among label overhead, routing table size, and path quality.

This work addresses the critical yet overlooked role of model capability profiling in large language model (LLM) routing. The authors propose RouteProfile, a framework that formulates LLM profiling as structured information integration over heterogeneous interaction histories. For the first time, it systematically decouples profile design from routing mechanisms and explores the profile design space across four dimensions: organizational form, representation type, aggregation depth, and learning configuration. Experiments demonstrate that structured profiles outperform flat ones, query-level signals surpass domain-level signals, and trainable structured profiles significantly enhance generalization to unseen models. Evaluations across three representative routers consistently validate the superiority of the proposed approach, establishing a foundation for fair comparison and principled design of LLM routing systems.

This work addresses the limitations of static penalty strategies in VLSI global routing, which struggle to adapt to complex congestion topologies and jointly optimize congestion, wirelength, and via count. To overcome these challenges, the paper proposes a dynamic multi-objective optimization framework that reformulates rip-up-and-reroute (R&R) as a dynamic system. The approach integrates SHAP-driven congestion decomposition, 3D Dijkstra maze routing, and an adaptive PathFinder algorithm, and—novelty introduced here—employs a large language model as a semantic policy optimizer to dynamically tune penalty parameters under knowledge graph constraints. Evaluated on the ISPD 2025 benchmarks, the method reduces MEMPOOL overflow by 98.6%, lowers ARIANE overflow to 146,109 (a 29.8× improvement over the state of the art), and achieves a penalty score of 0.0538, significantly outperforming the prior best result of 1.780.

This work proposes the $k$-step central shortest path problem, for which it designs a polynomial-time algorithm on unweighted graphs augmented with a novel pruning strategy, while proving the weighted variant to be NP-hard. The study introduces a new measure of reachability—quantified by the number of nodes adjacent to a path—and integrates it into shortest path optimization to jointly enhance path efficiency and coverage. The proposed framework also solves the closeness-central shortest path problem, which is shown to be NP-hard. Extensive experiments on synthetic and real-world networks with up to 2,000 nodes demonstrate the algorithm’s efficiency and scalability, revealing that the approach significantly improves coverage compared to strategies that merely extend the backbone path length.