Related papers: The Hierarchy of Saturating Matching Numbers
Machine teaching is an inverse problem of machine learning that aims at steering the student learner towards its target hypothesis, in which the teacher has already known the student's learning parameters. Previous studies on machine…
We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this…
The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given…
We consider max-weighted matching with costs for learning the weights, modeled as a "Pandora's Box" on each endpoint of an edge. Each vertex has an initially-unknown value for being matched to a neighbor, and an algorithm must pay some cost…
Many studies on the cost-sensitive learning assumed that a unique cost matrix is known for a problem. However, this assumption may not hold for many real-world problems. For example, a classifier might need to be applied in several…
Artificial intelligence is to teach machines to take actions like humans. To achieve intelligent teaching, the machine learning community becomes to think about a promising topic named machine teaching where the teacher is to design the…
The paper addresses a new class of combinatorial problems which consist in restructuring of solutions (as structures) in combinatorial optimization. Two main features of the restructuring process are examined: (i) a cost of the…
We consider the problem of minimizing cost among one-to-one assignments of $n$ jobs onto $n$ machines. The random assignment problem refers to the case when the cost associated with performing jobs on machines are random variables. Aldous…
We discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions. We consider the problem in a compact set with the topology both of the interval…
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. In this note we define a simple student-optimal criterion that is…
This work proposes a way to align statistical modeling with decision making. We provide a method that propagates the uncertainty in predictive modeling to the uncertainty in operational cost, where operational cost is the amount spent by…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the…
The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of…
Many applications require the collection of data on different variables or measurements over many system performance metrics. We term those broadly as measures or variables. Often data collection along each measure incurs a cost, thus it is…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate,…