An instance of the quadratic minimum spanning tree problem (QMSTP) is called linearizable if it can be rewritten as an instance of the linear minimum spanning tree problem in such a way that the objective function value is preserved at all feasible solutions. Previous work has shown that a sufficient condition for linearizability is that … Read more
We construct small extended formulations for nonnegative integer flows whose arc labels have a prescribed sum in a finite abelian group. For circulations, the formulation is a single integral network that combines cycles even when they lie in different components. This yields an O(Δn²) bound for strictly Δ-modular cographic integer hulls of translated cones, improving … Read more
This paper studies the single-machine problem of minimizing the weighted completion time variance (WCTV) and proposes a polynomially computable lower-bounding framework that generalizes the benchmark introduced by Nessah and Chu (2010). We first develop a generalized augmented-sequence decomposition that mathematically connects the weighted problem with the classical unweighted variance setting. Using this decomposition, we derive … Read more
The \(\textit{Colored Knapsack Problem}\) (ColKP) generalizes the classical Knapsack Problem by partitioning the items into color classes and requiring the selected items to admit an ordering in which consecutive items have different colors. The problem is weakly \(\mathcal{NP}\)-hard and admits two pseudo-polynomial dynamic programming (DP) algorithms proposed in the literature. These two DP algorithms have … Read more
Dynamic Discretisation Discovery (DDD) is a framework for solving a problem by iteratively solving and refining a relaxed version of the problem. DDD is the basis for state-of-the-art algorithms for various problems, including the continuous-time service network design problem (CTSNDP), which we study here. In the refinement step, such algorithms must identify conflicts in the … Read more
We show that every polytope $P\subseteq[0,1]^n$, and more generally every compact convex set, has Chv\’atal rank at most $12.22n^2+n\log_2 n+2n+4$. This improves the $O(n^2\log n)$ bound of Eisenbrand and Schulz and, together with the $\Omega(n^2)$ lower bound of Rothvo{\ss} and Sanit\`a, shows that the maximum Chv\’atal rank of a polytope in $[0,1]^n$ is $\Theta(n^2)$. More … Read more
State-of-the-art exact methods for the Maximum Cut problem are based on solving linear and semidefinite programming relaxations embedded into a branch-and-bound algorithm. For linear programming formulations, it was shown recently that it is thereby sufficient to enforce the integrality of the variables associated with the edges of a spanning tree. Our first contribution is to … Read more
We give an exact algorithm for minimizing an arbitrary rational quadratic polynomial xTQx+ cTx+ γ over the integer points of a bounded rational polyhedron Ax ≤b. For n variables and m inequalities, the running time is 2O(n log(n+1))(m+ 1)O(n)φ_{A,Q}^O(n)(1 + φ)O(1), where φ_{A,Q} is one plus the maximum binary encoding length of an entry of … Read more
This paper proposes an efficient Adaptive Large Neighborhood Search (ALNS) algorithm for the Flying Sidekick Traveling Salesman Problem (FSTSP). The algorithm integrates a stage-based truck–drone solution representation, two complementary destroy–repair operator groups, and six local-search neighborhoods focusing on drone operations and truck–drone interactions. Computational efficiency is enhanced through constant-time move evaluation after preprocessing and Static … Read more
We develop a few calculus rules to compute or lower bound the facial distance of a polytope. We illustrate our calculus rules on various popular polytopes. In particular, we provide a lower bound on the facial distance of the Birkhoff polytope. CitationWorking paper. Tepper School of Business. Carnegie Mellon UniversityArticleDownload View PDF