This paper studies task scheduling with unrelated crowd workers in mobile social networks, where the service time of a task depends on the crowd worker that performs it, and the objective is to minimize the total weighted completion time. For identical crowd workers, we tighten the approximation ratio of the Largest-Ratio-First (LRF) algorithm and update the competitive ratio of its online version. For unrelated crowd workers, we show that the time-indexed rounding framework of Im and Li remains valid when worker-dependent contact delays are added, which yields a randomized algorithm with an expected approximation ratio of 1.45; this improves upon the expected ratio of $1.5+ε$ obtained in our previous work for identical crowd workers. We also derandomize this algorithm. To improve computational efficiency, we further propose an algorithm that exploits the optimality of the Smith-ratio order on a single crowd worker, and we prove that it is a deterministic 1.5-approximation algorithm and that its polynomial-time version achieves an approximation ratio arbitrarily close to 1.5. Experiments on synthetic instances and on instances derived from real contact traces show that this algorithm outperforms three variants of LRF in all tested settings, with the largest advantage when the crowd workers are highly heterogeneous, performs on par with a local-search heuristic for unrelated machines, and is within 0.4\% of the optimum on average on small instances that can be solved exactly.
Coflows capture the collective communication requirements of data-parallel applications, and scheduling them well is essential to the performance of modern data centers. We study non-splitting coflow scheduling in a heterogeneous parallel network whose $m$ network cores may be Electronic Packet Switches (EPS), not-all-stop Optical Circuit Switches (OCS), or all-stop OCS, where every flow must be transmitted entirely through a single core. Previous approximation algorithms for this setting have guarantees that grow linearly with the number of cores $m$ or with the maximum flow degree $τ$ of a port, and therefore become weak as data centers deploy more cores. The source of this dependence is the rounding step: rounding each flow to the core holding its largest fractional value can inflate the load of a port by a factor of $m$. We replace this step with an iterative relaxation rounding scheme that handles the input-port and output-port capacity constraints simultaneously. For minimizing the makespan, this yields approximation ratios of $\min\{τ, 3\}$, $2\min\{τ, 3\}$, and $4\min\{τ, 3\}$ for pure EPS, pure not-all-stop OCS, and pure all-stop OCS networks, respectively. For minimizing the total weighted coflow completion time, we obtain approximation ratios of $8\min\{τ, 4\}$, $16\min\{τ, 4\}$, and $32\min\{τ, 4\}$ for the same three architectures. In a hybrid network, the guarantee is governed by the weakest architecture present, so the overall ratios are at most $4\min\{τ,3\}\le 12$ and $32\min\{τ,4\}\le 128$, respectively. Unlike all previous guarantees for non-splitting coflow scheduling in heterogeneous parallel networks, these bounds are absolute constants that do not grow with the number of cores $m$ or with the flow degree $τ$. We also show that the integrality gap of the underlying linear program is at least $2$.