Related papers: Introducing the Expohedron for Efficient Pareto-op…
Many online platforms, ranging from online retail stores to social media platforms, employ algorithms to optimize their offered assortment of items (e.g., products and contents). These algorithms often focus exclusively on achieving the…
We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu, Multilinear Pagerank, 2015], which is a system of quadratic equations with stochasticity and nonnegativity constraints. We use the theory of quadratic vector…
We study the fair allocation of indivisible goods and chores under ordinal valuations for agents with unequal entitlements. We show the existence and polynomial time computation of weighted necessarily proportional up to one item…
This paper studies how utility graphs decomposition algorithms can be used to effectively search for Pareto-efficient outcomes in complex automated negotiation. We propose a number of algorithms that can efficiently handle high-dimensional…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…
Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…
Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly…
We consider the allocation of indivisible objects among agents with different valuations, which can be positive or negative. An egalitarian allocation is an allocation that maximizes the smallest value given to an agent; finding such an…
We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective…
The Polytope Scheduling Problem (PSP) was introduced by Im, Kulkarni, and Munagala (JACM 2018) as a very general abstraction of resource allocation over time and captures many well-studied problems including classical unrelated machine…
The emerging edge computing paradigm promises to deliver superior user experience and enable a wide range of Internet of Things (IoT) applications. In this work, we propose a new market-based framework for efficiently allocating resources…
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
We study the problem of finding fair and efficient allocations of a set of indivisible items to a set of agents, where each item may be a good (positively valued) for some agents and a bad (negatively valued) for others, i.e., a mixed…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation,…
The Quadratic Assignment Problem (QAP) is a well-known NP-hard problem that is equivalent to optimizing a linear objective function over the QAP polytope. The QAP polytope with parameter $n$ - \qappolytope{n} - is defined as the convex hull…
In prediction-based decision-making systems, different perspectives can be at odds: The short-term business goals of the decision makers are often in conflict with the decision subjects' wish to be treated fairly. Balancing these two…
Pareto-optimality plays a central role in evaluating the efficiency of solutions to allocation problems, such as house allocation, school choice, and kidney exchange. We introduce a general linear programming problem subject to…
The rapid growth of wireless and mobile Internet has led to wide applications of exchanging resources over network, in which how to fairly allocate resources has become a critical challenge. To motivate sharing, a BD Mechanism is proposed…
Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the…