On the core of network synthesis games
Mathematical Programming: Series A and B
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
The connectivity carcass of a vertex subset in a graph and its incremental maintenance
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Minimum cuts in near-linear time
Journal of the ACM (JACM)
An alternate formulation of the symmetric traveling salesman problem and its properties
Discrete Applied Mathematics
Approximation algorithms
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Proving Integrality Gaps without Knowing the Linear Program
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Separating over Classes of TSP Inequalities Defined by 0 Node-Lifting in Polynominal Time
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
A fast algorithm for computing steiner edge connectivity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Compact vs. exponential-size LP relaxations
Operations Research Letters
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For a graph (V,E), existing compact linear formulations for the minimum cut problem require Θ(|V||E|) variables and constraints and can be interpreted as a composition of |V| − 1 polyhedra for minimum s-t cuts in much the same way as early approaches to finding globally minimum cuts relied on |V| − 1 calls to a minimum s-t cut algorithm. We present the first formulation to beat this bound, one that uses O(|V|2) variables and O(|V|3) constraints. An immediate consequence of our result is a compact linear relaxation with O(|V|2) constraints and O(|V|3) variables for enforcing global connectivity constraints. This relaxation is as strong as standard cut-based relaxations and has applications in solving traveling salesman problems by integer programming as well as finding approximate solutions for survivable network design problems using Jain's iterative rounding method. Another application is a polynomial-time verifiable certificate of size n for for the NP-complete problem of l1-embeddability of a rational metric on an n-set (as opposed to a certificate of size n2 known previously).