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We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving…
We consider a classic many-to-one matching setting, where participants need to be assigned to teams based on the preferences of both sides. Unlike most of the matching literature, we aim to provide fairness not only to participants, but…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
This article deals with ranking methods. We study the situation where a tournament between $n$ players $P_1$, $P_2$, \ldots $P_n$ gives the ranking $P_1 \succ P_2 \succ \cdots \succ P_n$, but, if the results of $P_n$ are no longer taken…
We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…
For over a decade now we have been witnessing the success of {\em massive parallel computation} (MPC) frameworks, such as MapReduce, Hadoop, Dryad, or Spark. One of the reasons for their success is the fact that these frameworks are able to…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
Scheduling problems are fundamental in combinatorial optimization. Much work has been done on approximation algorithms for NP-hard cases, but relatively little is known about exact solutions when some part of the input is a fixed parameter.…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are…
Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…
This paper presents an integer programming-based optimization framework designed to effectively address the complex final exam scheduling challenges encountered at Cornell University. With high flexibility, the framework is specifically…
Integer programming (IP) is a general optimization framework widely applicable to a variety of unstructured and structured problems arising in, e.g., scheduling, production planning, and graph optimization. As IP models many provably hard…
Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is…
Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…