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Is your Drupal site ready for Drupal 11?

Is your Drupal site ready for Drupal 11?

Is your Drupal site ready for Drupal 11? If you're on Drupal 10 or 9, the move to Drupal 11 is usually an upgrade. If you're on Drupal 7 or 8, it's a migration. Ei

Look-Ahead and Degree-Aware Branch-and-Bound for the Symmetric Traveling Salesman Problem: Algorithm, Complexity, and the Decisive Role of the Lower Bound

Look-Ahead and Degree-Aware Branch-and-Bound for the Symmetric Traveling Salesman Problem: Algorithm, Complexity, and the Decisive Role of the Lower Bound

LDA‑B&B is a branch‑and‑bound solver for symmetric TSP combining multi‑start nearest‑neighbour/2‑opt incumbents, look‑ahead and regret branch ordering, and a residual MST lower bound. The implementation contains a critical bug: the MST routine silently prunes the root node, returning a heuristic tour as proven optimal. After fixing this, the solver is exact but only up to ~20 cities. Look‑ahead and regret change node counts by 0.4% when optimality is proven. Replacing the MST bound with a Held–Karp 1‑tree bound dramatically improves performance: it reduces root gaps from 20–36% to 1% and proves random instances with 25 and 30 cities in 301 and 536 nodes. All eight small TSPLIB instances (n ≤ 42) are solved to optimality in under 4 seconds. Root bounds on mid‑size instances (1 060–2 319 cities) lie 0.5–2.2% below reference optima. Clustered instances remain hard. The study concludes that the lower bound, not branching heuristics, determines the exactness frontier.

India’s Top 100 FMCG Grocery Products and Brands: The Brands Shaping Everyday Indian Consumption

India’s Top 100 FMCG Grocery Products and Brands: The Brands Shaping Everyday Indian Consumption

This Listberg guide curates 100 prominent FMCG and grocery products shaping everyday Indian consumption, noting it is not an audited sales ranking. Items span staples (Amul, Tata Salt, Aashirvaad), packaged foods (Maggi), home and personal care (Surf Excel, Dove), beverages, and snacks, including Goa specialties. Key trends include kirana-led retail transformation, with e-commerce reaching 7% of national FMCG sales; branding of unbranded staples; convenience foods; dairy diversification; and regional preferences coexisting with national brands. While HUL and Nestlé dominate, smaller brands gain traction digitally. Success depends on availability, affordable packs, habit, trust, and regional relevance. Ultimately, India’s FMCG market is a complex mix of traditional and digital, mass-market and premium, and national and regional consumption, offering greater choice and complex competition.

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