Related papers: A min-max theorem for the minimum fleet-size probl…
It is well-known that the intersection of the matching polytope with a cardinality constraint is integral [8]. We prove a similar result for the polytope corresponding to the transportation problem with market choice (TPMC) (introduced in…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
For bipartite graphs the NP-completeness is proved for the problem of existence of maximum matching which removal leads to a graph with given lower(upper)bound for the cardinality of its maximum matching.
It is a celebrated result in early combinatorics that, in bipartite graphs, the size of maximum matching is equal to the size of a minimum vertex cover. K\H{o}nig's proof of this fact gave an algorithm for finding a minimum vertex cover…
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
The ridesharing problem is that given a set of trips, each trip consists of an individual, a vehicle of the individual and some requirements, select a subset of trips and use the vehicles of selected trips to deliver all individuals to…
An algorithm is presented which produces the minimum cost bipartite matching between two sets of M points each, where the cost of matching two points is proportional to the minimum distance by which a particle could reach one point from the…
As a rapidly expanding service, bike sharing is facing severe problems of bike over-supply and demand fluctuation in many Chinese cities. This study develops a large-scale method to determine the minimum fleet size under uncertainty, based…
We consider the platoon matching problem for a set of trucks with the same origin, but different destinations. It is assumed that the vehicles benefit from traveling in a platoon for instance through reduced fuel consumption. The vehicles…
The Maximum Carpool Matching problem is a star packing problem in directed graphs. Formally, given a directed graph $G = (V, A)$, a capacity function $ c: V \to N $, and a weight function $w : A \to R $, a feasible \emph{carpool matching}…
We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
In this paper we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an algorithm of Bertsimas and Sim (2003)…
We provide an explicit algorithm to solve the idempotent analogue of the discrete Monge-Kantorovich optimal mass transportation problem with the usual real number field replaced by the tropical (max-plus) semiring, in which addition is…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest that can not be extended. We show that this problem is hard to approximate with a constant smaller than 2, assuming…
For a vehicle on an assigned path, we find the minimum-time speed law that satisfies kinematic and dynamic constraints, related to maximum speed and maximum tangential and transversal acceleration. We present a necessary and sufficient…
Ride-pooling, which accommodates multiple passenger requests in a single trip, has the potential to significantly increase fleet utilization in shared mobility platforms. The ride-pooling assignment problem finds optimal co-riders to…