Several methods have been developed for joint working and spare capacity planning in survivable wavelength-division-multiplexing (WDM) networks. These methods have considered a static traffic demand and optimized the network cost assuming various cost models and survivability paradigms. Our interest primarily lies in network operation under dynamic traffic. We formulate various operational phas...

We consider binary pairwise graphical models and provide an exact characterization (necessary and sufficient conditions observing signs of potentials) of tightness for the LP relaxation on the triplet-consistent polytope of the MAP inference problem, by forbidding an odd-K5 (complete graph on 5 variables with all edges repulsive) as a signed minor in the signed suspension graph. This captures s...

We present a rating method that, given information on the pairwise comparisons of n items, minimizes the number of inconsistencies in the ranking of those items. Our Minimum Violations Ranking (MVR) Method uses a binary linear integer program (BILP) to do this. We prove conditions when the relaxed LP will give an optimal solution to the original BILP. In addition, the LP solution gives informat...

We study the quality of LP-based approximation methods for pure combinatorial problems. We found that the quality of the LPrelaxation is a direct function of the underlying constrainedness of the combinatorial problem. More specifically, we identify a novel phase transition phenomenon in the solution integrality of the relaxation. The solution quality of approximation schemes degrades substanti...

We consider the survivable network design problem the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-edge-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation...

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual requests (also called services) a common shared infrastructure and allocate resources meet diverse service requirements. The has been formulated as mixed integer linear programming (MILP) formulation in literature. We first novel (LP) relaxation of MILP formulation....

We consider the Survivable Network Design Problem (SNDP) and the Symmetric Traveling Salesman Problem (STSP). We give simpler proofs of the existence of a 2 -edge and 1-edge in any extreme point of the natural LP relaxations for the SNDP and STSP, respectively. We formulate a common generalization of both problems and show our results by a new counting argument. We also obtain a simpler proof o...

We consider the recent randomized 3 4 -algorithm for MAX SAT of Poloczek and Schnitger. We give a much simpler set of probabilities for setting the variables to true or false, which achieve the same expected performance guarantee. Our algorithm suggests a conceptually simple way to get a deterministic algorithm: rather than comparing to an unknown optimal solution, we instead compare the algori...

We study the Weighted Tree Augmentation Problem for general link costs. show that integrality gap of odd-LP relaxation (weighted) a k-level tree instance is at most 2−12k−1. For 2- and 3-level trees, these ratios are 32 74 respectively. Our proofs constructive yield polynomial-time approximation algorithms with matching guarantees.