Online weighted matching

Using a sensor network for distributed multi-robot task allocation

“…A decision epoch is a period of time during which only the alarms which have arrived are considered for assignment. It is shown in literature [17] that the optimal solution to online TA assigns the tasks in a greedy fashion. Also [17] show that the greedy online TA solution is within a bounded limit of an optimal solution obtained by offline TA.…”

“…It is shown in literature [17] that the optimal solution to online TA assigns the tasks in a greedy fashion. Also [17] show that the greedy online TA solution is within a bounded limit of an optimal solution obtained by offline TA. In general, increasing the decision epoch to infinity turns the online TA into offline TA problem.…”

Some recent results in the analysis of greedy algorithms for assignment problems

“…Let us finally return to the weighted bipartite matching problem, whose on-line complexity has been analyzed by Kalyanasundaram and Pruhs (1993). The model assumes an underlying complete bipartite graph Kn, ~ = (V1 w V2, E) on 2n vertices.…”

“…A surprising result of Bartal et al (1992) shows that the greedy algorithm for makespan minimization for job shop problems can measurably be beaten when one passes from pure list scheduling to balanced list scheduling. The situation is even worse for the greedy algorithm for the linear assignment problem, where the performance is an exponential factor off the online optimum (Kalyanasundaram and Pruhs (1993)). Boruvka (1926) showed that the greedy algorithm is successful provided J is a matroid, i.e., satisfies in addition to (2.0) and (2.1) It turns out that many structures in algorithmic combinatorics satisfy properties (2.0) and (2.2) but not necessarily (2.1) (e.g., the bisimplicial elimination schemes below).…”

On-Line Maximum Matching in Complete Multipartite Graphs with Implications to the Minimum ADM Problem on a Star Topology

“…The problem has found applications in other related problems (e.g., [ANR02], [AR05], [AC06]). The problem has also been studied for general weighted graphs in [KP93] where a 1/3-competitive deterministic algorithm is given. In [Sit96], a formula for the cardinality of the maximum matching in complete multipartite graph is given.…”