Lesser-Known Gems: Overlooked Algorithms Deserving More Attention
The Need for Exploration
In the fast-paced world of computer science research and innovation, algorithms come and go at a dizzying pace. The latest machine learning models generate buzz and capture attention, while other techniques get overlooked or forgotten. However, revisiting old or obscure algorithms can unlock substantial value.
Often algorithms fail to gain traction due to historical accidents – they were proposed just before a disruptive new method, the code or paper lacked widespread access, or the techniques addressed problems not yet deemed important. However, the intrinsic properties of these hidden gems may enable capabilities matching or exceeding modern alternatives. By dusting off and reevaluating neglected algorithms, researchers can discover optimal solutions for contemporary tasks.
This exploration benefits the field in multiple ways. First, adapting an old algorithm steers research in creative new directions, spurring innovation. The novel contexts stretch capabilities beyond original intentions. Second, resurrecting these overlooked ideas reduces redundant work solving problems with known solutions. Finally, expanded understanding of the algorithmic space allows more precise tool selection, elevating performance.
The sections below detail four remarkable but underappreciated algorithms poised to empower new applications.
Rediscovering the Satellite Tournament
The satellite tournament algorithm addresses leader selection in multi-agent scenarios. Proposed by Ogihara et al. in 2002, this method designates leaders through a knockout tournament system among distinct collaborative clusters. By alternating competition and cooperation phases, satellites converge on a communication hierarchy to improve coordination.
This technique displays several desirable attributes. First, satellite tournaments promote emergent leadership through decentralized self-organization, avoiding centralized control or explicit appointments. Second, the phased negotiation dynamic inherently balances exploration of alternatives with convergence on solutions. Finally, the satellite infrastructure readily scales to handle expanding groups.
While initially devised for distributed sensor nets, satellite tournament leadership empowers new coordination modes for robot swarms, smart cities, and team management. Code implementing the base algorithm follows:
def run_tournament(agents):
clusters = cluster_agents(agents)
for c in clusters:
leader = tournament(c)
c.set_leader(leader)
inter_cluster_hierarchy(clusters)
This snippet first groups agents into clusters, runs local tournaments to pick leaders, then builds the inter-cluster hierarchy. Extensions handle clustering methods, tournament brackets, and hierarchical assembly.
New Applications for the Greedy Set-Cover Algorithm
The set cover problem encompasses minimizing the cost to select sets covering all constituents of a universal set. Greedy set cover offers a simple yet effective approximation scheme choosing locally optimal sets. After sorting sets by coverage density, the algorithm incrementally picks the set adding the most uncovered elements.
Originally focused on abstract optimization, greedy set cover now captures diverse modern needs. Product package configuration for maximizing value integrates naturally as set cover. In machine learning, greedy subset selection produces compact, interpretable models without requiring full retraining. Even immunization planning against infectious outbreaks maps to efficiently covering population segments.
Though conceptually straightforward, theoretical analysis proves the greedy algorithm performs remarkably well. For set problems with coverage costs obeying diminishing returns assumptions, its solutions score within 1 + ln n of optimal using only polynomial time, n denoting set size. Implementing this versatile algorithm is straightforward:
def greedy_set_cover(universe, sets):
elements = sets[0]
covered = set()
cover = []
while covered != elements:
s = max_coverage_density(universe - covered)
cover.append(s)
covered |= s
return cover
The code iteratively selects the locally optimal set until full coverage is achieved, compiling the final cover. Variations exist for revisiting past decisions or handling constraints through the process.
The Power of Randomized Hill-Climbing
Hill climbing denotes incrementally traversing a space seeking peaks – locally optimal solutions. Simple hill climbing suffers from getting trapped at suboptimal peaks, but random restarts escape this fate. Randomly initialized hill climbing runs multiple times, picking the best peak discovered across attempts.
This algorithm applies to optimization problems where incremental improvement is possible but the landscape contains many poor local maxima. Though outperformed by specialized methods for some domains, randomized hill climbing provides a general-purpose technique. Reinforcement learning provides a salient use case – randomized climbing to discover policies, adding randomness to escape from plateaus.
Empirically, randomized climbing finds high-performing solutions relatively efficiently. Analytically, under common smoothness assumptions, the probability of getting trapped decays exponentially with restart attempts. These robust results often transfer to real-world spaces. Basic Python code implements one variant:
def random_hill_climb(problem, max_iters, restarts):
best_solution = None
best_value = -INF
for _ in range(restarts):
solution = random_initialization(problem)
value = objective(solution)
for _ in range(max_iters):
neighbor = get_random_neighbor(solution)
new_value = objective(neighbor)
if new_value > value:
solution = neighbor
value = new_value
if value > best_value:
best_solution = solution
best_value = value
return best_solution
This iterates over random restarts, running hill climbing from each start point and tracking the global best. Many enhancements integrate learning across attempts to boost performance.
Extending Lovász Local Lemma
The Lovász Local Lemma (LLL) provides probability tail bounds on avoiding all bad events in a set. If each event is relatively independent from others and unlikely individually, then with non-zero probability no events occur. Variants construct an object or process avoiding the full bad event set.
Since introduction in the 1970s, LLL enabled breakthroughs in combinatorics and computer science like non-deterministic algorithms. However, dependency assumptions limit applicability. Recent work by Kolipaka and Szegedy in 2011 established constructive LLL holds under local pairwise dependencies, expanding scope.
This extension now allows LLL application in areas like distributed computing with direct mutual communication rather than total independence. Researchers continue pushing dependency flexibility further. Though abstract, LLL also enables succinct probabilistic reasoning in complex environments like neural networks. Code applying LLL appears below:
def lll_avoid_all_bad_events(events, dependencies):
m = max(e.likelihood() for e in events)
if all(e has at most d local dependencies
and d * m < 1 for all e in events):
return construct_no_events(events)
else:
return "Criteria Not Met"
This first checks the dependency density upper bound criteria. If satisfied, then an object or process avoiding all events constructs. Theorem expansions focus on limiting reliance on ultra-low probability events in the criteria.
Conclusion
The algorithms showcased above - satellite tournament, greedy set cover, randomized hill climbing, and LLL - underscore the value in revisiting overlooked ideas. Beyond their initial applications, each supplies versatile techniques applicable to modern machine learning, optimization, and distributed systems challenges.
However, these examples only scratch the surface of forgotten gems in the vast algorithmic space. Continued exploration promises more powerful, efficient, and practical solutions. Researchers should dig deeper into algorithm history seeking inspiration, while learning limitations and contexts enabling resurrected methods to maximize impact.
