Distributed Task Allocation in Social Networks

1. Distributed Task Allocation in Social Networks Mathijs de Weerdt TU Delft, The Netherlands Joint work with Yingqian Zhang and Tomas Klos

2. Overview • The social task allocation problem • Complexity results • Greedy distributed protocol • Algorithm • Run-time analysis • Experiments • Conclusions

3. Motivation Social relations important in real-world task allocation: • Virtual organizations • Supply chain formation • File-sharing (P2P) networks • Free-lancers networks  preferred partnership instead of plain markets

4. Agent Social Network • Each agentAhas: • resourcesR • connectionsAE • tasks • Each taskThas • resourcesR • utility u • locationA agent a10Awith three tasksT (manager) agent a11A without tasks (contractor) connectionAE between two agents: allowed to allocate/cooperate

5. Social task allocation problem (STAP) Given an agent social network (A, AE) with • agentsA: with resources defined by rsc: A  R  N • tasksT: • with resource requirements rsc: T  R  N • with utility u: TR, and • with location loc: R  A find a validtask allocation: T  A  R  N while maximizing the sum of utilities of allocated tasks A validtask allocation: • required resources satisfied by resources of direct neighbors • no agent can sell more than its owned resources • for each task either none or all resources supplied

6. Complexity Hardness of problem: • The social task allocation problem (STAP) with an arbitrarysocial network is NP-complete. Hardness of approximation: • If degree of SN is bounded by , approximating STAP within a factor of is NP-hard for some Reason: although allocations are local, they are related.

7. Greedy distributed protocol (GDAP) Repeat • Each manager agent calculates the efficiency for its tasks ; sort tasks in descending order: • Each sends requests for most efficient task to neighbor agents . • Each compares and then offers available resources to task with highest efficiency. • Each checks whether all neighbors have offered and if task can be fully allocated, and informs neighbors. • When task t is allocated, remove it. Otherwise • if all neighbors offered resources, give up t: remove from • otherwise, try again. Until is empty for each manager agent.

8.  Greedy distributed protocol (GDAP) • e(t4)=9 • e(t0)=5 • e(t17)=1 • Each manager agent calculates the efficiency for its tasks ; sort tasks in descending order: • e(t19)=2 • e(t2)=6

9. Greedy distributed protocol (GDAP) help me with t4, e(t4)=9 • Each sends requests for most efficient task to neighboringagents . help me with t19, e(t19)=2 help me with t2, e(t2)=6

10. Greedy distributed protocol (GDAP) t4: r2 r2 r2 a10, I offer you for t4: r1 r3 • Each compares and then offers available resources to task with highest efficiency. t4: r1 • e(t4)=9 • e(t2)=6 • e(t19)=2 t4: r3 r4

11. Greedy distributed protocol (GDAP) a8: r1 • Each checks whether all neighbors have offered and if task can be fully allocated, and informs neighbors. a7: r3 r4 a11: r2 r2 r2

12. Greedy distributed protocol (GDAP) Repeat • Each manager agent calculates the efficiency for its tasks ; sort tasks in descending order: • Each sends requests for most efficient task to neighbor agents . • Each compares and then offers available resources to task with highest efficiency. • Each checks whether all neighbors have offered and if task can be fully allocated, and informs neighbors. • : When task t is allocated, remove it. Otherwise • if all neighbors offered resources, give up t: remove from • otherwise, try again. Until is empty for each manager agent.

13. Run-time analysis For a STAP with n tasks and m agents • O(n) iterations • per iteration: O(m) operations (in parallel) • so the run-time of GDAP is O(nm). • per iteration, per task O(m) messages • so number of communication messages is O(n2m).

14. Experiments • Objective: study performance of the greedy distributed algorithm GDAP in different problem settings Measurements • Computation time • Solution quality • for small problems: GDAP/OPT • for large problems: GDAP/Upper Bound

15. Experimental settings Social network structures • Small-world network(Watts, Strogatz, 1998): average shortest path length scales O(log n), even with few long links • Scale-free network(Barabasi, Albert, 1999): few agents have many neighbors; many have only a small number of neighbors • Random network(uniform): agents are randomly connected

16. Setting 1: 40 agents, 20 tasks, uniform task utilities, varying both resource ratio and degree

17. Setting 1a: 40 agents, 20 tasks, average network degree 6, uniform task utilities, varying resource ratio (total available resource / total required resource)

18. Setting 1b: 40 agents, 20 tasks, uniform task utilities, resource ratio 1.2, varying degree

19. Setting 2:resource ratio 1.2, degree 6, size ratio of agents and tasks 5/3, varying number of agents from 100 to 2000.

20. Conclusions • New variant of task allocation problem dealing with a social structure (STAP) • Distributed algorithm for STAP • Shown both theoretical and experimental results • Current work: • using referrals (mediators) and reputation • strategy-proof mechanism • studying real social networks