TL;DR: This paper obtains an O ( n 6 ) -time algorithm to find all Pareto optimal solutions of the bicriteria scheduling problem and solves the open problem of minimizing maximum lateness on the single bounded serial-batching machine.

TL;DR: New approximation algorithms with FPT time are presented which improve the known approximation guarantees for vehicle routing problems and aim to minimize the longest distance traveled by a vehicle denoted by λ.

TL;DR: This paper characterise q-critical graphs for all admissible values ofq and determine the exact values of q for which members of various infinite classes of graphs are q- critical.

TL;DR: A complete containment relationship between the closures of split, rank-2 split, cross, crooked cross and general multi-br branch split cuts is presented and it is shown that 3-branch split cuts strictly dominate crooked cross cuts, which in turn strictly dominate cross cuts.

TL;DR: This paper embeds hypercube and folded hypercube onto Cartesian product of trees such as 1-rooted complete binary tree and path, sibling tree and Path to minimize the wirelength.

TL;DR: This paper considers the multi-band robust knapsack problem which generalizes the ?

TL;DR: The first tableaux for defective Ramsey numbers are constructed with exact values whenever it is known, and lower and upper bounds otherwise, in light of defective cocoloring problem which consists of partitioning the vertex set of a given graph into k -sparse and k -dense sets.

TL;DR: A general algorithmic solution based on solving the problem variant without the cardinality constraint is presented and constant factor approximations depending on the solvability of this relaxation are obtained for a large class of submodular cost functions which are called value-monotone sub modular functions.

TL;DR: For small instances with box-constraints, it is shown that the resulting dual bounds are very tight; they can close a large percentage of the gap left open by both the RLT- and the SDP-relaxations of the problem.

TL;DR: It is proved that for hypercubes and some other symmetric graphs the player I I has a strategy to draw the game and complete bipartite graphs are considered as well.

TL;DR: This work shows how to construct a succinct representation, namely a piecewise-linear function φ approximating φ when given a black box access to an L -approximation oracle φ of φ (the oracle value is always within a multiplicative factor L from the true value).

TL;DR: A general method for deriving new inequalities for integer programming formulations of combinatorial optimization problems, motivated by local search algorithms, that can help in either pruning the search tree at some nodes or in improving the bound of the LP relaxations.

TL;DR: The structure of landmark sets for trees is analyzed and a linear time algorithm for finding a minimum cost landmark set for a given tree graph is designed.

TL;DR: A simple polynomial MULTIFIT-based algorithm, the schedules of which finish within 1.5 times the maximum between the latest end of a downtime and the end of the optimal schedule, when there is at most one downtime on each machine.

TL;DR: A study of the polytope defined by the minimizing form of the binary knapsack inequality, which is a greater-than-or-equal-to constraint, augmented by disjoint generalized upper bound constraints, and a set of valid inequalities called α -cover inequalities are characterized and dominance relationships among them are established.

TL;DR: This study adds new complexity results to the two standard objective functions under precedence constraints by discussing the complexities of several special cases for the number of late jobs and the total weighted completion time.

TL;DR: A new formulation is described to create optimal proportional symbol maps that maximizes one of two quality metrics: the total and the minimum visible length of disk boundaries.

TL;DR: This research generalises classic shortest path algorithms to network environments in which arc-costs are governed by functions, rather than fixed weights, and shows that the asymptotic efficiency of these algorithms is identical to their classic counterparts.

TL;DR: A mixed integer set which generalizes two well-known sets: the single node fixed-charge network set and the single arc design set is considered and several families of valid inequalities are derived that generalize the arc residual capacity inequalities and the flow cover inequalities.

TL;DR: A polyhedral study of a multi-commodity generalization of variable upper bound flow models is performed and a new family of inequalities is introduced, which generalizes traditional flow cover inequalities to the multi- commodity context.

TL;DR: In this paper, the authors describe the circuit polytope on series-parallel graphs and show the existence of a compact extended formulation of the circuit on planar graphs, which is based on the link between bonds and circuits.

TL;DR: This work uses the scaling idea together with transformation approach and uncertainty programming to develop a hybrid algorithm to optimize and obtain the uncertainty distribution of the total shipping cost.

TL;DR: This paper describes pack inequalities for the supermodular covering knapsack set and investigates their separation, extensions and lifting, and presents a computational study on using the polyhedral results derived for solving 0–1 optimization problems over conic quadratic constraints with a branch-and-cut algorithm.

TL;DR: A class of two-stage stochastic integer programs and their equivalent reformulation that uses the integer programming value functions in both stages that potentially alleviates this limitation of constraint-aggregation based approach.

TL;DR: The algorithm is designed to solve a more general class of multiflow problems, minimum cost node-demand multiflow problem, and is the first combinatorial polynomial time algorithm to this class of problems.

TL;DR: This note is meant to elucidate the difference between intersection cut as originally defined, and intersection cuts as defined in the more recent literature.

TL;DR: A feasibility condition is derived for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows.

TL;DR: This work strengthens the linearised IP-formulation by cutting planes that are derived from facets of the corresponding matching problem where only one quadratic term is present in the objective function (QMP1) by adopting the reformulation linearisation technique (RLT).