In Greek mythology, Arceisius (also Arcesius or Arkeisios) was the forefather of the Ithacan royal house — father of Laertes and grandfather of Odysseus. Homer makes Zeus shape the dynasty so that each generation bore but a single son until Telemachus, and the suitors' plot to destroy the race of godlike Arceisius drives much of the Odyssey's anxiety about the extinction of Odysseus' line.
Adapted from Wikipedia, "Arcesius" · CC BY-SA 4.0
I.Family
Homer names Arceisius as father of Laertes and ancestor of Odysseus and Telemachus in a house that ran in a single male line. Later mythographers supply other parentages — Zeus and Euryodeia in scholia on the Odyssey, Cephalus in several genealogies, or Cephalus and Procris in Hyginus — and a wife Chalcomedusa as mother of Laertes in some accounts. The patronymic Arceisiades marks Laertes and Odysseus as sons of his line.
II.In the Odyssey
Telemachus recounts how Cronos' son fashioned their house: Arceisius begot Laertes alone, Laertes begot Odysseus alone, and Odysseus left Telemachus the sole heir — until suitors filled the halls and plotted the prince's death so that the name of godlike Arceisius might perish from Ithaca.
When Odysseus at last stood with Laertes and Telemachus against the kin of the slain wooers, Athena addressed the old king as Son of Arceisius and breathed strength into him to cast his spear beside son and grandson.