Workload balancing strategies for parallel Subset Sum

The gap

Evidence profile

Stated in the synthesized section of the source papers, classified as general, drawn from work published between 1990 and 2026, spanning 5 journals. Those papers have been cited 3 times in total.

Supporting evidence — 8 representative gaps

• An integer linear programming formulation and genetic algorithm for the maximum set splitting problem (2012) · Publications de l Institut Mathematique · doi

  Comparative performance evaluation of parallel metaheuristic approaches (genetic algorithms, particle swarm optimization) on Subset Sum is absent; [2] and [4] study these methods on related combinatorial problems (set splitting, knapsack) but [4] reveals convergence failures in set-based PSO, and neither evaluates scalability or parallel efficiency on Subset Sum instances.

  generalstated in synthesizedevidence 5/5
  Keywords: comparative performance evaluation parallel metaheuristic approaches genetic algorithms
• Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics (1990) · Management Science · doi

  No study combines dual heuristics with parallel branch-and-bound for Subset Sum; [6] demonstrates dual LP relaxation heuristics for set covering/partitioning problems, but parallelization of this bounding strategy and its interaction with parallel search on Subset Sum remain unexplored.

  generalstated in synthesizedevidence 5/5
  Keywords: study combines dual heuristics parallel branch-and-bound subset sum
• Traveling salesman problem parallelization by solving clustered subproblems (2023) · Foundations of Computing and Decision Sciences · cited 3× · doi

  Scalability thresholds and problem size requirements for efficient parallel Subset Sum solving are undefined; [9] identifies that TSP parallelization requires ≥1000 nodes for efficiency, but no analogous analysis exists for Subset Sum problem dimensions and parallel speedup characteristics.

  generalstated in synthesizedevidence 5/5
  Keywords: scalability thresholds problem size requirements efficient parallel subset
• An integer linear programming formulation and genetic algorithm for the maximum set splitting problem (2012) · Publications de l Institut Mathematique · doi

  Genetic algorithms [5] and heuristic-based parallelization [12] show promise for combinatorial problems, but no work applies genetic algorithms or population-based parallel methods to the subset sum problem specifically, leaving open whether such approaches can compete with exact parallel methods.

  generalstated in synthesizedevidence 5/5
  Keywords: genetic algorithms heuristic-based parallelization show promise combinatorial problems
• Index Dependent Nested Loops Parallelization with an Even Distributed Number of Steps (2021) · Informatica · doi

  No systematic study of load balancing strategies for nested-loop parallelization of Subset Sum enumeration algorithms; [7] addresses index-dependent nested loop partitioning for even workload distribution, but does not apply this to the specific structure and dependencies of Subset Sum search trees or dynamic programming approaches.

  generalstated in synthesizedevidence 5/5
  Keywords: systematic study load balancing strategies nested-loop parallelization subset
• Optimal Solution of Set Covering/Partitioning Problems Using Dual Heuristics (1990) · Management Science · doi

  No exploration of hybrid parallel algorithms combining exact methods (branch-and-bound) with heuristic acceleration for Subset Sum; [8] demonstrates hybrid evolutionary methods for scheduling, but Subset Sum lacks a comparable hybrid framework that leverages both lower bounds from dual relaxations ([6]) and parallel metaheuristic search.

  generalstated in synthesizedevidence 5/5
  Keywords: exploration hybrid parallel algorithms combining exact methods branch-and-bound
• Index Dependent Nested Loops Parallelization with an Even Distributed Number of Steps (2021) · Informatica · doi

  Workload balancing strategies for parallel Subset Sum solvers are unexplored; [7] addresses load distribution for nested loops with index-dependent iterations, but no method exists to apply or adapt such techniques to the irregular search tree structure of Subset Sum algorithms.

  generalstated in synthesizedevidence 4/5
  Keywords: workload balancing strategies parallel subset sum solvers unexplored
• A hybrid approach to multi-objective unrelated parallel machine scheduling with a new interpretation of job batches and families (2026) · Soft Computing · doi

  Hybrid parallel approaches combining exact and heuristic methods for Subset Sum are not investigated; [8] demonstrates hybrid evolutionary methods for scheduling but does not address Subset Sum, and no paper explores parallel branch-and-bound with parallel metaheuristic lower bounds for Subset Sum.

  generalstated in synthesizedevidence 4/5
  Keywords: hybrid parallel approaches combining exact heuristic methods subset

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