Motivated by team formation applications , we study discrete optimization problems of the form \max_{S\in\mathcal{S}}%DIFDELCMD < \left(%%% f(S)-w(S)%DIFDELCMD < \right)%%% , where f:2^{V}%DIFDELCMD < \to%%% \mathbb{R_{+} is a non-negative monotone submodular function, w:2^{V}}%DIFDELCMD < \to%%% \mathbb{R_{+} is a non-negative linear function , and S}%DIFDELCMD < \subseteq2%%% ^{V. We give very simple and efficient algorithms for classical constraints, such as cardinality and matroid, that work in a variety of models, including the offline, online, and streaming. Our algorithms use a very simple scaling approach: we pick an absolute constant c}%DIFDELCMD < \geq1 %%% and optimize the function f(S)-c\cdot w(S) using a black-box application of standard algorithms , such as the classical Greedy algorithm and the single-threshold Greedy algorithm. These algorithms are based on recent works that use (time varying) scaling combined with classical algorithms such as the discrete and continuous Greedy algorithms (Feldman, WADS'19; Harshawet al. , ICML'19) .
Motivated by }}%DIFDELCMD < \left(%%% %DIFDELCMD < \right)%%% }%DIFDELCMD < \to%%% } is a non-negative monotone submodular function, w:2^{V}}%DIFDELCMD < \to%%% _{+} is a non-negative linear function , and S}%DIFDELCMD < \subseteq2%%% . We give very simple and efficient algorithms for classical constraints, such as cardinality and matroid, that work in a variety of models, including the offline, online, and streaming. Our algorithms use a very simple scaling approach: we pick an absolute constant c}%DIFDELCMD < \geq1 %%% online crowdsourcing platforms as well as applications that span human-resource management in industrial and URLanizations researchers have studied extensively the team-formation problem. This problem has been primarily formalized as an optimization problem where the goal is to optimize some metric of the team performance, subject to the constraint that the team members should cover all the skills required by the task. In this paper, we generalize this problem formulation and set as our objective to optimize a function that maximizes the coverage of skills minus the cost of the corresponding team. This formulation appears as a more natural one, particularly in cases where one needs to strike a balance between the coverage achieved and the cost being paid. To the best of our knowledge we are the first to formalize the team-formation problem in this manner. From the algorithmic perspective, we demonstrate that by using simple variants of the standard greedy algorithm (used for submodular optimization) we can design algorithms that have provable approximation guarantees, are extremely efficient and work very well in practice. Our experiments with real data from online crowdsourcing platforms demonstrate the efficiency and the efficacy of our methods. Finally, we believe that our problem formulation and algorithms are of independent interest and can be used in many applications where there is a submodular objective and a linear cost .
D
team formation applications , we study discrete optimization problems of the form \max_{S\in\mathcal{S
D
f(S)-w(S)
D
, where f:2^{V
D
\mathbb{R_{+
D
\mathbb{R
D
^{V
R
and optimize the function f(S)-c\cdot w(S) using a black-box application of standard
online crowdsourcing platforms as well as applications that span human-resource management in industrial and URLanizations researchers have studied extensively the team-formation problem. This problem has been primarily formalized as an optimization problem where the goal is to optimize some metric of the team performance, subject to the constraint that the team members should cover all the skills required by the task. In this paper, we generalize this problem formulation and set as our objective to optimize a function that maximizes the coverage of skills minus the cost of the corresponding team. This formulation appears as a more natural one, particularly in cases where one needs to strike a balance between the coverage achieved and the cost being paid. To the best of our knowledge we are the first to formalize the team-formation problem in this manner. From the algorithmic perspective, we demonstrate that by using simple variants of the standard greedy algorithm (used for submodular optimization) we can design algorithms that have provable approximation guarantees, are extremely efficient and work very well in practice. Our experiments with real data from online crowdsourcing platforms demonstrate the efficiency and the efficacy of our methods. Finally, we believe that our problem formulation and
D
, such as the classical Greedy algorithm and the single-threshold Greedy algorithm. These algorithms are based on recent works that use (time varying) scaling combined with classical algorithms such as the discrete and continuous Greedy algorithms (Feldman, WADS'19; Harshaw
D
et al.
R
, ICML'19)
are of independent interest and can be used in many applications where there is a submodular objective and a linear cost