Title: Ahimelech
Content:  Ahimelech (אֲחִימֶ֫לֶך ’Ăḥîmeleḵ, "brother of a king"), the son of Ahitub and father of Abiathar, but described as the son of Abiathar in and in four places in 1 Chronicles. He descended from Aaron's son Ithamar and the High Priest of Israel Eli. In his name is Abimelech according to the Masoretic Text, and is probably the same as Ahiah.
Title: Ammihud
Content: The father of the Ephraimite chief Elishama, the father of Nun, at the time of the Exodus (Book of Numbers ; ; ). ; The father of Shemuel, of the Tribe of Simeon ; The father of Pedahel, a prince of the Tribe of Naphtali ; The father of Talmai, king of Geshur, to whom Absalom fled after the murder of Amnon (2 Samuel ) ; The son of Omri, and the father of Uthai (1 Chronicles ) Ammihud (עַמִּיהוּד ‘Ammîhūḏ, "people of glory" or "renowned") is the name of several Hebrew Bible figures:
Title: Abimelech
Content: Abimelech, son of Gideon, proclaimed king after the death of his father. ; The father of Abiathar, and high priest in the time of David. In the parallel passage, the name is given as Ahimelech; most authorities consider this the more correct reading. ; The king of Gath better known as Achish, referred to as Abimelech or Achimelech in the title of Psalm 34. ; The husband of Naomi, and father of Mahlon and Chilion who leaves Bethlehem and dies in the land of Moab, in the Hebrew, his name is given as Elimelek, which is likely the correct reading. Abimélech, Satrap of Gaza is a character baritone in Saint-Saëns' Samson and Delilah. Apart from the king (or kings) of Gerar, the Bible also records this name for: Other literary references include:
Title: Abimelech (Judges)
Content:  Abimelech (אֲבִימֶלֶךְ ’Ǎḇīmeleḵ) was the king of Shechem and a son of biblical judge Gideon. His name can best be interpreted as "my father is king", claiming the inherited right to rule. He is introduced in as the son of Gideon and his Shechemite concubine, and the biblical account of his reign is described in chapter nine of the Book of Judges. According to the Bible, he was an unprincipled and ambitious ruler, often engaged in war with his own subjects.
Title: Ahimelech
Content:  Ahimelech's death was seen as a partial fulfilment of the curse on the House of Eli – that none of Eli's male descendants would live to old age; the other part of the curse on the House of Eli – that the priesthood would pass out of his descendants – was fulfilled when Abiathar was deposed from the office of High Priest. Rabbinical literature linked the extermination of the male descendants of David with the extermination of the priests of Nob by Saul - deeming it divine retribution because David's action had provoked Saul's outburst - and also linked the survival of David's descendant Joash with that of Ahimelech's son Abiathar.
Title: Ahijah
Content:  same probably as Ahimelech, who was High Priest at Nob in the reign of Saul (1 Sam. 22:11) and at Shiloh, where the Tabernacle was set up. Some, however, suppose that Ahimelech was the brother of Ahijah, and that they both officiated as high priests, Ahijah at Gibeah or Kirjath-jearim, and Ahimelech at Nob. ; 8) Father of King Baasha of Israel Ahijah (אֲחִיָּה ’Ǎḥîyāh, "brother of Yah"; Latin and Douay–Rheims: Ahias) is a name of several biblical individuals:  A man named Ahijah also appears in the Babylonian Talmud in the 2nd century AD as one of the first Babylonian Exilarchs.
Title: List of minor Old Testament figures, A–K
Content:  Ahisamach or Ahisamakh, also Ahis'amach (Hebrew: אחיסמך "brother of support"), of the tribe of Dan, was the father of Aholiab according to Exodus 31:6, Exodus 35:34, and Exodus 38:23.
Title: Ahimelech
Content:  He was the twelfth High Priest, and officiated at Nob, where he was visited by David (he gave David and his companions five loaves of the showbread) when David fled from Saul. He was summoned into Saul's presence, and accused of disloyalty for assisting David, on the information of Doeg the Edomite. Then the king commanded that he, with the other priests who stood beside him, 86 in all, should be slain with his family. This sentence was carried into execution by Doeg in a cruel manner. Possibly Abiathar had a son also called Ahimelech, or the two names, as some think, may have been accidentally transposed in ;, marg.; 24:3, 6, 31.
Title: Avimelekh
Content:  Avimelekh (Авимеле́х) is a Russian male first name. It was included into various, often handwritten, church calendars throughout the 17th–19th centuries, but was omitted from the official Synodal Menologium at the end of the 19th century. It is derived from the Biblical Hebrew Abimelech (lit. my father—a king).
Title: Ahitub (father of Zadok)
Content:  Ahitub (אֲחִיטוּב ’Aḥiṭub, or ’Aḥiṭuv, "my brother is goodness") was the father of Zadok ([http://www.biblegateway.com/passage/?search=2%20Sam.%208:15-17;&version=9; 2 Sam. 8:15-17]). This Ahitub was the son of Amariah, Amarias or Arophaeus, who was the son of Meraioth, Meraoith or Merahoth, who was the son of Zerahiah or Zaraias, who was the son of Uzzi, who was the son of Bukki, who was the son of Abishua, who was the son of Phinehas, who was the son of Eleazar, who was the son of Aaron (1 Chronicles 6:3-8). There is a faint possibility that this Ahitub was made high priest by Saul after the extermination of the family of Ahimelech, but it is very unlikely as there are apparently no references supporting this. It is much more likely that Saul had no official high priest after this incident until the end of his reign (see Josephus's Antiquities of the Jews, Book VI, Chapter XII, Paragraph 7.

Question: Who is the father of Ahimelech?
Answer: Ahitub.