Abstract. 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 → N, and a weight function w : A → R, a feasible carpool matching is a triple (P, D, M ), where P (passengers) and D (drivers) form a partition of V , and M is a subset of A ∩ (P × D), under the constraints that for every vertex In the Maximum Carpool Matching problem we seek for a matching (P, D, M ) that maximizes the total weight of M . The problem arises when designing an online carpool service, such as Zimride [1], that tries to connect between passengers and drivers based on (arbitrary) similarity function. The problem is known to be NP-hard, even for uniform weights and without capacity constraints. We present a 3-approximation algorithm for the problem and 2-approximation algorithm for the unweighted variant of the problem.
For the Maximum Carpool Matching problem, a 0.33-approximation algorithm and a 0.5-approximation algorithm for both the general problem and the unweighted variant are given in REF .
Approximation Algorithms for the Maximum Carpool Matching Problem
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Mathematics Computer Science